diff options
Diffstat (limited to 'libs/math/doc/sf_and_dist/html/math_toolkit/special')
64 files changed, 632 insertions, 69 deletions
diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html index fd978d390d..1e92928adc 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html @@ -40,7 +40,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html index 32742e7314..fc23e89f17 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html @@ -681,7 +681,7 @@ are also computed by recursions (involving gamma functions), but <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html index 2cd6a5560f..5ead6c678a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html @@ -199,7 +199,7 @@ is also known as the <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html index 71227de8d1..5d6adc8a12 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html @@ -472,7 +472,7 @@ are also computed by recursions (involving gamma functions), but <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html index 9464c277c0..8bd007accd 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html @@ -7,7 +7,7 @@ <link rel="home" href="../../../index.html" title="Math Toolkit"> <link rel="up" href="../bessel.html" title="Bessel Functions"> <link rel="prev" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds"> -<link rel="next" href="../ellint.html" title="Elliptic Integrals"> +<link rel="next" href="../hankel.html" title="Hankel Functions"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> @@ -20,7 +20,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="mbessel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="mbessel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../hankel.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section math_toolkit_special_bessel_sph_bessel"> <div class="titlepage"><div><div><h4 class="title"> @@ -142,7 +142,7 @@ for small <span class="emphasis"><em>x</em></span>: <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> @@ -150,7 +150,7 @@ for small <span class="emphasis"><em>x</em></span>: </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="mbessel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="mbessel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../hankel.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html index 6ff012c1fc..f4760ebf66 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html @@ -6,7 +6,7 @@ <meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> <link rel="home" href="../../index.html" title="Math Toolkit"> <link rel="up" href="../special.html" title="Special Functions"> -<link rel="prev" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds"> +<link rel="prev" href="hankel/sph_hankel.html" title="Spherical Hankel Functions"> <link rel="next" href="ellint/ellint_intro.html" title="Elliptic Integral Overview"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> @@ -20,7 +20,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="hankel/sph_hankel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section math_toolkit_special_ellint"> <div class="titlepage"><div><div><h3 class="title"> @@ -42,7 +42,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> @@ -50,7 +50,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="hankel/sph_hankel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html index 18426706a9..c096ca02e2 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html @@ -254,7 +254,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html index bafbe2b12d..e124a8fc57 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html @@ -254,7 +254,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index 53bdd07adc..6b6e33dcc7 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -308,7 +308,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html index f69f4f8d9b..dbc8d5ad3c 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html @@ -428,7 +428,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html index fb1c94a351..b65ccd86a8 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html @@ -394,7 +394,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint.html index ab9718c875..7297239be2 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint.html @@ -36,7 +36,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 4e1a18f261..79ad1377a1 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -287,7 +287,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index dd94895f80..bf87a9991b 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -282,7 +282,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html index 0734b3f3aa..976b1c5b05 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html @@ -42,7 +42,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html index b364dc8b4a..c525b11dbb 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html @@ -133,7 +133,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html index ddd30492a4..779003b067 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html @@ -142,7 +142,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html index 279978ce93..d4731e1408 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html @@ -185,7 +185,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html index 09c7080474..3dcb4d48af 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html @@ -98,7 +98,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html index c8fed1cc6b..809abcd4dc 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html @@ -102,7 +102,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel.html new file mode 100644 index 0000000000..c37dc139a7 --- /dev/null +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel.html @@ -0,0 +1,50 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Hankel Functions</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../index.html" title="Math Toolkit"> +<link rel="up" href="../special.html" title="Special Functions"> +<link rel="prev" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds"> +<link rel="next" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hankel/cyl_hankel.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section math_toolkit_special_hankel"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="math_toolkit.special.hankel"></a><a class="link" href="hankel.html" title="Hankel Functions">Hankel Functions</a> +</h3></div></div></div> +<div class="toc"><dl> +<dt><span class="section"><a href="hankel/cyl_hankel.html">Cyclic Hankel + Functions</a></span></dt> +<dt><span class="section"><a href="hankel/sph_hankel.html">Spherical Hankel + Functions</a></span></dt> +</dl></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hankel/cyl_hankel.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html new file mode 100644 index 0000000000..b4e890ea80 --- /dev/null +++ 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name="math_toolkit.special.hankel.cyl_hankel"></a><a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">Cyclic Hankel + Functions</a> +</h4></div></div></div> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h0"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.synopsis"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.synopsis">Synopsis</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">cyl_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">cyl_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">cyl_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">cyl_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&);</span> +</pre> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h1"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.description"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.description">Description</a> + </h5> +<p> + The functions <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a> + and <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_2</a> + return the result of the <a href="http://dlmf.nist.gov/10.2#P3" target="_top">Hankel + functions</a> of the first and second kind respectively: + </p> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>cyl_hankel_1(v, x) = H<sub>v</sub><sup>(1)</sup>(x) = J<sub>v</sub>(x) + i Y<sub>v</sub>(x)</em></span> + </p></blockquote></div> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>cyl_hankel_2(v, x) = H<sub>v</sub><sup>(2)</sup>(x) = J<sub>v</sub>(x) - i Y<sub>v</sub>(x)</em></span> + </p></blockquote></div> +<p> + where: + </p> +<p> + <span class="emphasis"><em>J<sub>v</sub>(x)</em></span> is the Bessel function of the first kind, and + <span class="emphasis"><em>Y<sub>v</sub>(x)</em></span> is the Bessel function of the second kind. + </p> +<p> + The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result + type calculation rules</em></span></a> when T1 and T2 are different types. + The functions are also optimised for the relatively common case that T1 + is an integer. + </p> +<p> + The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>. + </p> +<p> + Note that while the arguments to these functions are real values, the results + are complex. That means that the functions can only be instantiated on + types <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span> + <span class="keyword">double</span></code>. The functions have also + been extended to operate over the whole range of <span class="emphasis"><em>v</em></span> + and <span class="emphasis"><em>x</em></span> (unlike <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> + and <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>). + </p> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h2"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.performance"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.performance">Performance</a> + </h5> +<p> + These functions are generally more efficient than two separate calls to + the underlying Bessel functions as internally Bessel J and Y can be computed + simultaneously. + </p> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h3"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.testing"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.testing">Testing</a> + </h5> +<p> + There are just a few spot tests to exercise all the special case handling + - the bulk of the testing is done on the Bessel functions upon which these + are based. + </p> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h4"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.accuracy"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.accuracy">Accuracy</a> + </h5> +<p> + Refer to <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> + and <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>. + </p> +<h5> +<a name="math_toolkit.special.hankel.cyl_hankel.h5"></a> + <span><a name="math_toolkit.special.hankel.cyl_hankel.implementation"></a></span><a class="link" href="cyl_hankel.html#math_toolkit.special.hankel.cyl_hankel.implementation">Implementation</a> + </h5> +<p> + For <span class="emphasis"><em>x < 0</em></span> the following reflection formulae are + used: + </p> +<p> + <a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/16/01/01/" target="_top"> + <span class="inlinemediaobject"><img src="../../../../equations/hankel1.png"></span></a> + </p> +<p> + <a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/" target="_top"> + <span class="inlinemediaobject"><img src="../../../../equations/hankel2.png"></span></a> + </p> +<p> + <a href="http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/" target="_top"> + <span class="inlinemediaobject"><img src="../../../../equations/hankel3.png"></span></a> + </p> +<p> + Otherwise the implementation is trivially in terms of the Bessel J and + Y functions. + </p> +<p> + Note however, that the Hankel functions compute the Bessel J and Y functions + simultaneously, and therefore a single Hankel function call is more efficient + than two Bessel function calls. The one exception is when <span class="emphasis"><em>v</em></span> + is a small positive integer, in which case the usual Bessel function routines + for integer order are used. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="../hankel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hankel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="sph_hankel.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html new file mode 100644 index 0000000000..b7779eddf2 --- /dev/null +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html @@ -0,0 +1,122 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Spherical Hankel Functions</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../../index.html" title="Math Toolkit"> +<link rel="up" href="../hankel.html" title="Hankel Functions"> +<link rel="prev" href="cyl_hankel.html" title="Cyclic Hankel Functions"> +<link rel="next" href="../ellint.html" title="Elliptic Integrals"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../index.html">Home</a></td> +<td 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name="math_toolkit.special.hankel.sph_hankel"></a><a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">Spherical Hankel + Functions</a> +</h4></div></div></div> +<h5> +<a name="math_toolkit.special.hankel.sph_hankel.h0"></a> + <span><a name="math_toolkit.special.hankel.sph_hankel.synopsis"></a></span><a class="link" href="sph_hankel.html#math_toolkit.special.hankel.sph_hankel.synopsis">Synopsis</a> + </h5> +<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">sph_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">sph_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">sph_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span> +<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">></span> <span class="identifier">sph_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&);</span> +</pre> +<h5> +<a name="math_toolkit.special.hankel.sph_hankel.h1"></a> + <span><a name="math_toolkit.special.hankel.sph_hankel.description"></a></span><a class="link" href="sph_hankel.html#math_toolkit.special.hankel.sph_hankel.description">Description</a> + </h5> +<p> + The functions <a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_1</a> + and <a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_2</a> + return the result of the <a href="http://dlmf.nist.gov/10.47#P1" target="_top">spherical + Hankel functions</a> of the first and second kind respectively: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../equations/hankel4.png"></span> + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../equations/hankel5.png"></span> + </p> +<p> + The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result + type calculation rules</em></span></a> when T1 and T2 are different types. + The functions are also optimised for the relatively common case that T1 + is an integer. + </p> +<p> + The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>. + </p> +<p> + Note that while the arguments to these functions are real values, the results + are complex. That means that the functions can only be instantiated on + types <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span> + <span class="keyword">double</span></code>. The functions have also + been extended to operate over the whole range of <span class="emphasis"><em>v</em></span> + and <span class="emphasis"><em>x</em></span> (unlike <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> + and <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>). + </p> +<h5> +<a name="math_toolkit.special.hankel.sph_hankel.h2"></a> + <span><a name="math_toolkit.special.hankel.sph_hankel.testing"></a></span><a class="link" href="sph_hankel.html#math_toolkit.special.hankel.sph_hankel.testing">Testing</a> + </h5> +<p> + There are just a few spot tests to exercise all the special case handling + - the bulk of the testing is done on the Bessel functions upon which these + are based. + </p> +<h5> +<a name="math_toolkit.special.hankel.sph_hankel.h3"></a> + <span><a name="math_toolkit.special.hankel.sph_hankel.accuracy"></a></span><a class="link" href="sph_hankel.html#math_toolkit.special.hankel.sph_hankel.accuracy">Accuracy</a> + </h5> +<p> + Refer to <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> + and <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>. + </p> +<h5> +<a name="math_toolkit.special.hankel.sph_hankel.h4"></a> + <span><a name="math_toolkit.special.hankel.sph_hankel.implementation"></a></span><a class="link" href="sph_hankel.html#math_toolkit.special.hankel.sph_hankel.implementation">Implementation</a> + </h5> +<p> + These functions are trivially implemented in terms of <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a> + and <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_2</a>. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="cyl_hankel.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hankel.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html index 2214015229..af3e29f019 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html @@ -37,7 +37,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html index 6b883fafd4..2140a9e046 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html @@ -117,7 +117,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html index e247fba0dd..a1d386ffc4 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html @@ -112,7 +112,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html index 8a614a30f5..6df001bed1 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html @@ -7,7 +7,7 @@ <link rel="home" href="../../../index.html" title="Math Toolkit"> <link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions"> <link rel="prev" href="asinh.html" title="asinh"> -<link rel="next" href="../../utils.html" title="Floating Point Utilities"> +<link rel="next" href="../owens_t.html" title="Owen's T function"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> @@ -20,7 +20,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="asinh.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../utils.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="asinh.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../owens_t.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section math_toolkit_special_inv_hyper_atanh"> <div class="titlepage"><div><div><h4 class="title"> @@ -122,7 +122,7 @@ denoting <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> @@ -130,7 +130,7 @@ denoting </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="asinh.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../utils.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="asinh.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../owens_t.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html index 1d6b7dc431..d6579df647 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html @@ -100,7 +100,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/owens_t.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/owens_t.html new file mode 100644 index 0000000000..a80c5febaf --- /dev/null +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/owens_t.html @@ -0,0 +1,230 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Owen's T function</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../index.html" title="Math Toolkit"> +<link rel="up" href="../special.html" title="Special Functions"> +<link rel="prev" href="inv_hyper/atanh.html" title="atanh"> +<link rel="next" href="../utils.html" title="Floating Point Utilities"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="inv_hyper/atanh.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../utils.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section math_toolkit_special_owens_t"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="math_toolkit.special.owens_t"></a><a class="link" href="owens_t.html" title="Owen's T function">Owen's T function</a> +</h3></div></div></div> +<h5> +<a name="math_toolkit.special.owens_t.h0"></a> + <span><a name="math_toolkit.special.owens_t.synopsis"></a></span><a class="link" href="owens_t.html#math_toolkit.special.owens_t.synopsis">Synopsis</a> + </h5> +<p> +</p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">owens_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> +</pre> +<p> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> +<a class="link" href="../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">owens_t</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">h</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">a</span><span class="special">);</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">></span> +<a class="link" href="../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">owens_t</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">h</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">&);</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<h5> +<a name="math_toolkit.special.owens_t.h1"></a> + <span><a name="math_toolkit.special.owens_t.description"></a></span><a class="link" href="owens_t.html#math_toolkit.special.owens_t.description">Description</a> + </h5> +<p> + Returns the <a href="http://en.wikipedia.org/wiki/Owen%27s_T_function" target="_top">Owens_t + function</a> of <span class="emphasis"><em>h</em></span> and <span class="emphasis"><em>a</em></span>. + </p> +<p> + The final <a class="link" href="../policy.html" title="Policies">Policy</a> argument is optional + and can be used to control the behaviour of the function: how it handles + errors, what level of precision to use etc. Refer to the <a class="link" href="../policy.html" title="Policies">policy + documentation for more details</a>. + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../equations/owens_t.png"></span> + </p> +<p> + <span class="inlinemediaobject"><img src="../../../graphs/plot_owens_t.png" alt="plot_owens_t"></span> + </p> +<p> + The function <code class="computeroutput"><span class="identifier">owens_t</span><span class="special">(</span><span class="identifier">h</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> gives the probability of the event <span class="emphasis"><em>(X + > h and 0 < Y < a * X)</em></span>, where <span class="emphasis"><em>X</em></span> + and <span class="emphasis"><em>Y</em></span> are independent standard normal random variables. + </p> +<p> + For h and a > 0, T(h,a), gives the volume of an uncorrelated bivariate + normal distribution with zero means and unit variances over the area between + <span class="emphasis"><em>y = ax</em></span> and <span class="emphasis"><em>y = 0</em></span> and to the right + of <span class="emphasis"><em>x = h</em></span>. + </p> +<p> + That is the area shaded in the figure below (Owens 1956). + </p> +<p> + <span class="inlinemediaobject"><img src="../../../graphs/owens_integration_area.png" align="middle"></span> + </p> +<p> + and is also illustrated by a 3D plot. + </p> +<p> + <span class="inlinemediaobject"><img src="../../../graphs/plot_owens_3d_xyp.png" alt="plot_owens_3d_xyp"></span> + </p> +<p> + This function is used in the computation of the <a class="link" href="../dist/dist_ref/dists/skew_normal_dist.html" title="Skew Normal Distribution">Skew + Normal Distribution</a>. It is also used in the computation of bivariate + and multivariate normal distribution probabilities. The return type of this + function is computed using the <a class="link" href="../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result + type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and type + T otherwise. + </p> +<p> + Owen's original paper (page 1077) provides some additional corner cases. + </p> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>T(h, 0) = 0</em></span> + </p></blockquote></div> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>T(0, a) = ½π arctan(a)</em></span> + </p></blockquote></div> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>T(h, 1) = ½ G(h) [1 - G(h)]</em></span> + </p></blockquote></div> +<div class="blockquote"><blockquote class="blockquote"><p> + <span class="emphasis"><em>T(h, ∞) = G(|h|)</em></span> + </p></blockquote></div> +<p> + where G(h) is the univariate normal with zero mean and unit variance integral + from -∞ to h. + </p> +<h5> +<a name="math_toolkit.special.owens_t.h2"></a> + <span><a name="math_toolkit.special.owens_t.accuracy"></a></span><a class="link" href="owens_t.html#math_toolkit.special.owens_t.accuracy">Accuracy</a> + </h5> +<p> + Over the built-in types and range tested, errors are less than 10 * std::numeric_limits<RealType>::epsilon(). + </p> +<h5> +<a name="math_toolkit.special.owens_t.h3"></a> + <span><a name="math_toolkit.special.owens_t.testing"></a></span><a class="link" href="owens_t.html#math_toolkit.special.owens_t.testing">Testing</a> + </h5> +<p> + Test data was generated by Patefield and Tandy algorithms T1 and T4, and + also the suggested reference routine T7. + </p> +<div class="itemizedlist"><ul class="itemizedlist" type="disc"> +<li class="listitem"> + T1 was rejected if the result was too small compared to <code class="computeroutput"><span class="identifier">atan</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code> + (ie cancellation), + </li> +<li class="listitem"> + T4 was rejected if there was no convergence, + </li> +<li class="listitem"> + Both were rejected if they didn't agree. + </li> +</ul></div> +<p> + Over the built-in types and range tested, errors are less than 10 std::numeric_limits<RealType>::epsilon(). + </p> +<p> + However, that there was a whole domain (large <span class="emphasis"><em>h</em></span>, small + <span class="emphasis"><em>a</em></span>) where it was not possible to generate any reliable + test values (all the methods got rejected for one reason or another). + </p> +<p> + There are also two sets of sanity tests: spot values are computed using + <a href="http://www.wolfram.com/products/mathematica/index.html" target="_top">Wolfram + Mathematica</a> and <a href="http://www.r-project.org/" target="_top">The R Project + for Statistical Computing</a>. + </p> +<h5> +<a name="math_toolkit.special.owens_t.h4"></a> + <span><a name="math_toolkit.special.owens_t.implementation"></a></span><a class="link" href="owens_t.html#math_toolkit.special.owens_t.implementation">Implementation</a> + </h5> +<p> + The function was proposed and evaluated by <a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177728074" target="_top">Donald. + B. Owen, Tables for computing bivariate normal probabilities, Ann. Math. + Statist., 27, 1075-1090 (1956)</a>. + </p> +<p> + The algorithms of Patefield, M. and Tandy, D. "Fast and accurate Calculation + of Owen's T-Function", Journal of Statistical Software, 5 (5), 1 - 25 + (2000) are adapted for C++ with arbitrary RealType. + </p> +<p> + The Patefield-Tandy algorithm provides six methods of evalualution (T1 to + T6); the best method is selected according to the values of <span class="emphasis"><em>a</em></span> + and <span class="emphasis"><em>h</em></span>. See the original paper and the source in <a href="../../../../../../../boost/math/special_functions/owens_t.hpp" target="_top">owens_t.hpp</a> + for details. + </p> +<p> + The Patefield-Tandy algorithm is accurate to approximately 20 decimal places, + so for types with greater precision we use: + </p> +<div class="itemizedlist"><ul class="itemizedlist" type="disc"> +<li class="listitem"> + A modified version of T1 which folds the calculation of <span class="emphasis"><em>atan(h)</em></span> + into the T1 series (to avoid subtracting two values similar in magnitude), + and then accelerates the resulting alternating series using method 1 + from H. Cohen, F. Rodriguez Villegas, D. Zagier, "Convergence acceleration + of alternating series", Bonn, (1991). The result is valid everywhere, + but doesn't always converge, or may become too divergent in the first + few terms to sum accurately. This is used for <span class="emphasis"><em>ah < 1</em></span>. + </li> +<li class="listitem"> + A modified version of T2 which is accelerated in the same manner as T1. + This is used for <span class="emphasis"><em>h > 1</em></span>. + </li> +<li class="listitem"> + A version of T4 only when both T1 and T2 have failed to produce an accurate + answer. + </li> +<li class="listitem"> + Fallback to the Patefiled Tandy algorithm when all the above methods + fail: this happens not at all for our test data at 100 decimal digits + precision. However, there is a difficult area when <span class="emphasis"><em>a</em></span> + is very close to 1 and the precision increases which may cause this to + happen in very exceptional circumstances. + </li> +</ul></div> +<p> + Using the above algorithm and a 100-decimal digit type, results accurate + to 80 decimal places were obtained in the difficult area where <span class="emphasis"><em>a</em></span> + is close to 1, and greater than 95 decimal places elsewhere. + </p> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="inv_hyper/atanh.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../utils.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers.html index 6a45209361..19307c0125 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers.html @@ -41,7 +41,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html index e530d2ae69..15be4ffa1d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html @@ -84,7 +84,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html index 3e1f64d13b..af35730140 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html @@ -250,7 +250,7 @@ improving the implementation. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html index 8c0a01bbbe..414973e33a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html @@ -93,7 +93,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html index ef982a1401..56a162888f 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html @@ -74,7 +74,7 @@ in such a <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html index 1d6ad4fc7f..3ed0735f8e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html @@ -106,7 +106,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html index 904ef5cc0e..04cb2a3440 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html @@ -86,7 +86,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html index 53baed1b13..bd73cda147 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html @@ -89,7 +89,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html index b8e43dba94..d97dbc9ca1 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html @@ -39,7 +39,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html index 7358817ef6..4afd714dc8 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html @@ -89,7 +89,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html index f827336c1b..2e6166c58d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html @@ -314,7 +314,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html index 9dfcae7210..d96fb135a1 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html @@ -967,7 +967,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html index c1f3c9ed09..a0d993c6ea 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html @@ -519,7 +519,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html index 11a476f2eb..289fa95404 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html @@ -35,7 +35,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html index ac612136b6..906c9b065c 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html @@ -617,7 +617,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html index 5457e06f40..43f849fa3a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html @@ -191,7 +191,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html index 55271e8d6f..68016cd663 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html @@ -43,7 +43,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html index 410016ad30..f46620983e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html @@ -374,7 +374,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html index daa5b5eb73..7415251ac9 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html @@ -94,7 +94,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html index a977340667..04181110e1 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html @@ -343,7 +343,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html index 6a9d40a558..a7f1dbce73 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html @@ -1035,7 +1035,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html index 113afe3502..d72923af94 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html @@ -245,7 +245,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html index 6b3920ca8f..5786ff3e8e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html @@ -467,7 +467,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html index 7365df9d21..d0c7d6766f 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html @@ -454,7 +454,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html index 923d7fcb05..7be55ec5c9 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html @@ -38,7 +38,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html index 023630cc8a..422966d082 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html @@ -269,7 +269,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html index 853a1bdda4..290de0bc9e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html @@ -443,7 +443,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html index 1419484363..fc14a2831c 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html @@ -697,7 +697,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html index 63546490de..0d2432d312 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html @@ -296,7 +296,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html index 15a2801c44..5b4a51d63b 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html @@ -37,7 +37,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html index 857ea2a469..02932e9a69 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html @@ -67,7 +67,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html index 1486d6141c..5985d4f96e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html @@ -66,7 +66,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html index 9a89b14e06..150c1decdd 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html @@ -70,7 +70,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html index eaa3e26e91..f1d7663614 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -31,7 +31,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index db21b3fe92..cfd61a2b9a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -299,7 +299,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> |