1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Hypergeometric 2F0</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../hypergeometric.html" title="Hypergeometric Functions"> 9<link rel="prev" href="hypergeometric_0f1.html" title="Hypergeometric 0F1"> 10<link rel="next" href="hypergeometric_1f1.html" title="Hypergeometric 1F1"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="hypergeometric_0f1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.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="hypergeometric_1f1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.hypergeometric.hypergeometric_2f0"></a><a class="link" href="hypergeometric_2f0.html" title="Hypergeometric 2F0">Hypergeometric 28 <sub>2</sub><span class="emphasis"><em>F</em></span><sub>0</sub></a> 29</h3></div></div></div> 30<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">hypergeometric_2F0</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 31 32<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> 33 34<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> <span class="identifier">T3</span><span class="special">></span> 35<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">);</span> 36 37<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> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span> 38<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> 39 40<span class="special">}}</span> 41</pre> 42<h5> 43<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h0"></a> 44 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.description"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.description">Description</a> 45 </h5> 46<p> 47 The function <code class="computeroutput"><span class="identifier">hypergeometric_2F0</span></code> 48 returns the result of 49 </p> 50<div class="blockquote"><blockquote class="blockquote"><p> 51 <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0.svg"></span> 52 53 </p></blockquote></div> 54<p> 55 The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result 56 type calculation rules</em></span></a> when <code class="computeroutput"><span class="identifier">T1</span></code> 57 and <code class="computeroutput"><span class="identifier">T2</span></code> are different types. 58 </p> 59<p> 60 The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can 61 be used to control the behaviour of the function: how it handles errors, 62 what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy 63 documentation for more details</a>. 64 </p> 65<p> 66 The functions return the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a> 67 whenever the result is undefined or complex. The valid domain for this function 68 occurs only when one of <code class="computeroutput"><span class="identifier">a1</span></code> 69 or <code class="computeroutput"><span class="identifier">a2</span></code> is a negative integer: 70 ie the polynomial case. 71 </p> 72<h5> 73<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h1"></a> 74 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.implementation"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.implementation">Implementation</a> 75 </h5> 76<p> 77 When <code class="computeroutput"><span class="identifier">a1</span> <span class="special">==</span> 78 <span class="identifier">a2</span> <span class="special">-</span> 79 <span class="number">0.5</span></code> then the function is implemented 80 in terms of the Hermite polynomial: 81 </p> 82<div class="blockquote"><blockquote class="blockquote"><p> 83 <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_hermite.svg"></span> 84 85 </p></blockquote></div> 86<p> 87 When both <code class="computeroutput"><span class="identifier">a1</span></code> and <code class="computeroutput"><span class="identifier">a2</span></code> are integers then the function is implemented 88 in terms of the associated-Laguerre polynomial: 89 </p> 90<div class="blockquote"><blockquote class="blockquote"><p> 91 <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_laguerre.svg"></span> 92 93 </p></blockquote></div> 94<p> 95 If the defining series is divergent, we use the continued fraction 96 </p> 97<div class="blockquote"><blockquote class="blockquote"><p> 98 <span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_cf.svg"></span> 99 100 </p></blockquote></div> 101<p> 102 Otherwise we use the defining series. 103 </p> 104</div> 105<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 106<td align="left"></td> 107<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 108 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 109 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 110 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 111 Daryle Walker and Xiaogang Zhang<p> 112 Distributed under the Boost Software License, Version 1.0. (See accompanying 113 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>) 114 </p> 115</div></td> 116</tr></table> 117<hr> 118<div class="spirit-nav"> 119<a accesskey="p" href="hypergeometric_0f1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.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="hypergeometric_1f1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 120</div> 121</body> 122</html> 123
