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<title>Derivative of the Incomplete Beta Function</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.sf_beta.beta_derivative"></a><a class="link" href="beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the
Incomplete Beta Function</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.sf_beta.beta_derivative.h0"></a>
<span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.synopsis"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.synopsis">Synopsis</a>
</h5>
<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">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
</pre>
<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> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">></span>
<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">ibeta_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">b</span><span class="special">,</span> <span class="identifier">T3</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> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
<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">ibeta_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">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.sf_beta.beta_derivative.h1"></a>
<span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.description"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.description">Description</a>
</h5>
<p>
This function finds some uses in statistical distributions: it computes the
partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete
beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>.
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/derivative2.svg"></span>
</p>
<p>
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
type calculation rules</em></span></a> when T1, T2 and T3 are different
types.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">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="Chapter 14. Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<h5>
<a name="math_toolkit.sf_beta.beta_derivative.h2"></a>
<span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.accuracy"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.accuracy">Accuracy</a>
</h5>
<p>
Almost identical to the incomplete beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>.
</p>
<h5>
<a name="math_toolkit.sf_beta.beta_derivative.h3"></a>
<span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.implementation"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.implementation">Implementation</a>
</h5>
<p>
This function just expose some of the internals of the incomplete beta function
<a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>: refer to
the documentation for that function for more information.
</p>
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Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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