1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Hypergeometric 1F0</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.html" title="Hypergeometric Functions"> 10<link rel="next" href="hypergeometric_0f1.html" title="Hypergeometric 0F1"> 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.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_0f1.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_1f0"></a><a class="link" href="hypergeometric_1f0.html" title="Hypergeometric 1F0">Hypergeometric 28 <sub>1</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_1F0</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_1F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</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_1F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</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_1f0.h0"></a> 44 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_1f0.description"></a></span><a class="link" href="hypergeometric_1f0.html#math_toolkit.hypergeometric.hypergeometric_1f0.description">Description</a> 45 </h5> 46<p> 47 The function <code class="computeroutput"><span class="identifier">hypergeometric_1F0</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_1f0.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 for <code class="computeroutput"><span class="identifier">z</span> <span class="special">==</span> <span class="number">1</span></code> 68 or <code class="computeroutput"><span class="number">1</span> <span class="special">-</span> 69 <span class="identifier">z</span> <span class="special"><</span> 70 <span class="number">0</span></code> and <code class="computeroutput"><span class="identifier">a</span></code> 71 not an integer. 72 </p> 73<h5> 74<a name="math_toolkit.hypergeometric.hypergeometric_1f0.h1"></a> 75 <span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_1f0.implementation"></a></span><a class="link" href="hypergeometric_1f0.html#math_toolkit.hypergeometric.hypergeometric_1f0.implementation">Implementation</a> 76 </h5> 77<p> 78 The implementation is trivial: 79 </p> 80<div class="blockquote"><blockquote class="blockquote"><p> 81 <span class="serif_italic"><span class="emphasis"><em><sub>1</sub>F<sub>0</sub>(a, z) = (1-z)<sup>-a</sup></em></span></span> 82 </p></blockquote></div> 83</div> 84<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 85<td align="left"></td> 86<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 87 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 88 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 89 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 90 Daryle Walker and Xiaogang Zhang<p> 91 Distributed under the Boost Software License, Version 1.0. (See accompanying 92 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>) 93 </p> 94</div></td> 95</tr></table> 96<hr> 97<div class="spirit-nav"> 98<a accesskey="p" href="../hypergeometric.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_0f1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 99</div> 100</body> 101</html> 102
