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4<title>Derivative of the Incomplete Gamma Function</title>
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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">&lt;</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">&gt;</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">&lt;</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">&gt;</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">&lt;</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">&gt;</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">&amp;);</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>
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95      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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97      Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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