1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Hypergeometric 0F1</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_1f0.html" title="Hypergeometric 1F0"> 10<link rel="next" href="hypergeometric_2f0.html" title="Hypergeometric 2F0"> 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_1f0.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_2f0.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_0f1"></a><a class="link" href="hypergeometric_0f1.html" title="Hypergeometric 0F1">Hypergeometric 28 <sub>0</sub><span class="emphasis"><em>F</em></span><sub>1</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_0F1</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> 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_0F1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</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> <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_0F1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</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> <span class="comment">// namespaces</span> 41</pre> 42<h5> 43<a name="math_toolkit.hypergeometric.hypergeometric_0f1.h0"></a> 44 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_0f1.description"></a></span><a class="link" href="hypergeometric_0f1.html#math_toolkit.hypergeometric.hypergeometric_0f1.description">Description</a> 45 </h5> 46<p> 47 The function <code class="computeroutput"><span class="identifier">hypergeometric_0F1</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_0f1.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. This occurs only when <code class="computeroutput"><span class="identifier">b</span></code> is an integer <= 0. 68 </p> 69<h5> 70<a name="math_toolkit.hypergeometric.hypergeometric_0f1.h1"></a> 71 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_0f1.implementation"></a></span><a class="link" href="hypergeometric_0f1.html#math_toolkit.hypergeometric.hypergeometric_0f1.implementation">Implementation</a> 72 </h5> 73<p> 74 The function is implemented via its defining series wherever convergent. 75 </p> 76<p> 77 For a divergent series we use the continued fraction as long as the result 78 is not too small: 79 </p> 80<div class="blockquote"><blockquote class="blockquote"><p> 81 <span class="inlinemediaobject"><img src="../../../equations/hyper_0f1_cf.svg"></span> 82 83 </p></blockquote></div> 84<p> 85 and one of the Bessel function relations otherwise: 86 </p> 87<div class="blockquote"><blockquote class="blockquote"><p> 88 <span class="inlinemediaobject"><img src="../../../equations/hyper_0f1_bessel_j.svg"></span> 89 90 </p></blockquote></div> 91<div class="blockquote"><blockquote class="blockquote"><p> 92 <span class="inlinemediaobject"><img src="../../../equations/hyper_0f1_bessel_i.svg"></span> 93 94 </p></blockquote></div> 95</div> 96<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 97<td align="left"></td> 98<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 99 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 100 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 101 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 102 Daryle Walker and Xiaogang Zhang<p> 103 Distributed under the Boost Software License, Version 1.0. (See accompanying 104 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>) 105 </p> 106</div></td> 107</tr></table> 108<hr> 109<div class="spirit-nav"> 110<a accesskey="p" href="hypergeometric_1f0.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_2f0.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 111</div> 112</body> 113</html> 114
