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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&#160;15.&#160;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&#160;15.&#160;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 <p>
  56         <span class="inlinemediaobject"><img src="../../../equations/derivative1.svg"></span>
  57       </p>
  58 <p>
  59         The final <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
  60         be used to control the behaviour of the function: how it handles errors,
  61         what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">policy
  62         documentation for more details</a>.
  63       </p>
  64 <p>
  65         Note that the derivative of the function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
  66         can be obtained by negating the result of this function.
  67       </p>
  68 <p>
  69         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
  70         type calculation rules</em></span></a> when T1 and T2 are different types,
  71         otherwise the return type is simply T1.
  72       </p>
  73 <h5>
  74 <a name="math_toolkit.sf_gamma.gamma_derivatives.h2"></a>
  75         <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>
  76       </h5>
  77 <p>
  78         Almost identical to the incomplete gamma function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>:
  79         refer to the documentation for that function for more information.
  80       </p>
  81 <h5>
  82 <a name="math_toolkit.sf_gamma.gamma_derivatives.h3"></a>
  83         <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>
  84       </h5>
  85 <p>
  86         This function just expose some of the internals of the incomplete gamma function
  87         <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>: refer to the
  88         documentation for that function for more information.
  89       </p>
  90 </div>
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  92 <td align="left"></td>
  93 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  94       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  95       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  96       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  97         Distributed under the Boost Software License, Version 1.0. (See accompanying
  98         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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