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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="id1083704"></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="id1083988"></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="id1084072"></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="id1084100"></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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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| 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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