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<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.special.sf_gamma.gamma_derivatives"></a><a class="link" href="gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function"> Derivative
of the Incomplete Gamma Function</a>
</h4></div></div></div>
<a name="math_toolkit.special.sf_gamma.gamma_derivatives.synopsis"></a><h5>
<a name="id1087634"></a>
<a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.synopsis">Synopsis</a>
</h5>
<p>
</p>
<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>
</pre>
<p>
</p>
<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>
<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>
<a class="link" href="../../main_overview/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">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="Policies">Policy</a><span class="special">></span>
<a class="link" href="../../main_overview/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="Policies">Policy</a><span class="special">&);</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<a name="math_toolkit.special.sf_gamma.gamma_derivatives.description"></a><h5>
<a name="id1087918"></a>
<a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.description">Description</a>
</h5>
<p>
This function find some uses in statistical distributions: it implements
the partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete
gamma function.
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../equations/derivative1.png"></span>
</p>
<p>
</p>
<p>
The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
is optional and can be used to control the behaviour of the function:
how it handles errors, what level of precision to use etc. Refer to the
<a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
</p>
<p>
</p>
<p>
Note that the derivative of the function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
can be obtained by negating the result of this function.
</p>
<p>
The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
type calculation rules</em></span></a> when T1 and T2 are different types,
otherwise the return type is simply T1.
</p>
<a name="math_toolkit.special.sf_gamma.gamma_derivatives.accuracy"></a><h5>
<a name="id1088002"></a>
<a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.accuracy">Accuracy</a>
</h5>
<p>
Almost identical to the incomplete gamma function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>:
refer to the documentation for that function for more information.
</p>
<a name="math_toolkit.special.sf_gamma.gamma_derivatives.implementation"></a><h5>
<a name="id1088030"></a>
<a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.implementation">Implementation</a>
</h5>
<p>
This function just expose some of the internals of the incomplete gamma
function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>:
refer to the documentation for that function for more information.
</p>
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Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
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