1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Derivative of the Incomplete Gamma Function</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="../sf_gamma.html" title="Gamma Functions"> 9<link rel="prev" href="igamma_inv.html" title="Incomplete Gamma Function Inverses"> 10<link rel="next" href="../factorials.html" title="Factorials and Binomial Coefficients"> 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="igamma_inv.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.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="../factorials.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.sf_gamma.gamma_derivatives"></a><a class="link" href="gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of 28 the Incomplete Gamma Function</a> 29</h3></div></div></div> 30<h5> 31<a name="math_toolkit.sf_gamma.gamma_derivatives.h0"></a> 32 <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.synopsis"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.synopsis">Synopsis</a> 33 </h5> 34<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">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 35</pre> 36<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> 37 38<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> 39<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">gamma_p_derivative</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">x</span><span class="special">);</span> 40 41<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> 42<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">gamma_p_derivative</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">x</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> 43 44<span class="special">}}</span> <span class="comment">// namespaces</span> 45</pre> 46<h5> 47<a name="math_toolkit.sf_gamma.gamma_derivatives.h1"></a> 48 <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.description"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.description">Description</a> 49 </h5> 50<p> 51 This function find some uses in statistical distributions: it implements 52 the partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete 53 gamma function. 54 </p> 55<div class="blockquote"><blockquote class="blockquote"><p> 56 <span class="inlinemediaobject"><img src="../../../equations/derivative1.svg"></span> 57 58 </p></blockquote></div> 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 Note that the derivative of the function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a> 67 can be obtained by negating the result of this function. 68 </p> 69<p> 70 The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result 71 type calculation rules</em></span></a> when T1 and T2 are different types, 72 otherwise the return type is simply T1. 73 </p> 74<h5> 75<a name="math_toolkit.sf_gamma.gamma_derivatives.h2"></a> 76 <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.accuracy"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.accuracy">Accuracy</a> 77 </h5> 78<p> 79 Almost identical to the incomplete gamma function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>: 80 refer to the documentation for that function for more information. 81 </p> 82<h5> 83<a name="math_toolkit.sf_gamma.gamma_derivatives.h3"></a> 84 <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.implementation"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.implementation">Implementation</a> 85 </h5> 86<p> 87 This function just expose some of the internals of the incomplete gamma function 88 <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>: refer to the 89 documentation for that function for more information. 90 </p> 91</div> 92<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 93<td align="left"></td> 94<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 95 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 96 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 97 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 98 Daryle Walker and Xiaogang Zhang<p> 99 Distributed under the Boost Software License, Version 1.0. (See accompanying 100 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>) 101 </p> 102</div></td> 103</tr></table> 104<hr> 105<div class="spirit-nav"> 106<a accesskey="p" href="igamma_inv.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.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="../factorials.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 107</div> 108</body> 109</html> 110