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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.hypergeometric.hypergeometric_2f0"></a><a class="link" href="hypergeometric_2f0.html" title="Hypergeometric 2F0">Hypergeometric
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<sub>2</sub><span class="emphasis"><em>F</em></span><sub>0</sub></a>
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</h3></div></div></div>
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<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">hypergeometric_2F0</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<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>
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<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>
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<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">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">);</span>
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<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 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
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<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">hypergeometric_2F0</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</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">&);</span>
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<span class="special">}}</span>
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</pre>
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<h5>
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<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h0"></a>
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<span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.description"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.description">Description</a>
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</h5>
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<p>
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The function <code class="computeroutput"><span class="identifier">hypergeometric_2F0</span></code>
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returns the result of
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/hyper_2f0.svg"></span>
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</p></blockquote></div>
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<p>
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The return type of these functions is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
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type calculation rules</em></span></a> when <code class="computeroutput"><span class="identifier">T1</span></code>
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and <code class="computeroutput"><span class="identifier">T2</span></code> are different types.
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</p>
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<p>
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The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
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be used to control the behaviour of the function: how it handles errors,
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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
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documentation for more details</a>.
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</p>
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<p>
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The functions return the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
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whenever the result is undefined or complex. The valid domain for this function
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occurs only when one of <code class="computeroutput"><span class="identifier">a1</span></code>
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or <code class="computeroutput"><span class="identifier">a2</span></code> is a negative integer:
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ie the polynomial case.
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</p>
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<h5>
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<a name="math_toolkit.hypergeometric.hypergeometric_2f0.h1"></a>
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<span class="phrase"><a name="math_toolkit.hypergeometric.hypergeometric_2f0.implementation"></a></span><a class="link" href="hypergeometric_2f0.html#math_toolkit.hypergeometric.hypergeometric_2f0.implementation">Implementation</a>
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</h5>
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<p>
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When <code class="computeroutput"><span class="identifier">a1</span> <span class="special">==</span>
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<span class="identifier">a2</span> <span class="special">-</span>
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<span class="number">0.5</span></code> then the function is implemented
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in terms of the Hermite polynomial:
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_hermite.svg"></span>
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</p></blockquote></div>
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<p>
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When both <code class="computeroutput"><span class="identifier">a1</span></code> and <code class="computeroutput"><span class="identifier">a2</span></code> are integers then the function is implemented
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in terms of the associated-Laguerre polynomial:
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_laguerre.svg"></span>
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</p></blockquote></div>
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<p>
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If the defining series is divergent, we use the continued fraction
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/hyper_2f0_cf.svg"></span>
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</p></blockquote></div>
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<p>
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Otherwise we use the defining series.
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</p>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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