ceph/src/boost/libs/math/doc/html/math_toolkit/hankel/sph_hankel.html

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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.hankel.sph_hankel"></a><a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">Spherical Hankel Functions</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.hankel.sph_hankel.h0"></a>
  31         <span class="phrase"><a name="math_toolkit.hankel.sph_hankel.synopsis"></a></span><a class="link" href="sph_hankel.html#math_toolkit.hankel.sph_hankel.synopsis">Synopsis</a>
  32       </h5>
  33 <pre class="programlisting"><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>
  34 <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</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="special">&gt;</span> <span class="identifier">sph_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
  35
  36 <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>
  37 <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</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="special">&gt;</span> <span class="identifier">sph_hankel_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</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>
  38
  39 <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>
  40 <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</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="special">&gt;</span> <span class="identifier">sph_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
  41
  42 <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>
  43 <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</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="special">&gt;</span> <span class="identifier">sph_hankel_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</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>
  44 </pre>
  45 <h5>
  46 <a name="math_toolkit.hankel.sph_hankel.h1"></a>
  47         <span class="phrase"><a name="math_toolkit.hankel.sph_hankel.description"></a></span><a class="link" href="sph_hankel.html#math_toolkit.hankel.sph_hankel.description">Description</a>
  48       </h5>
  49 <p>
  50         The functions <a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_1</a>
  51         and <a class="link" href="sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_2</a> return
  52         the result of the <a href="http://dlmf.nist.gov/10.47#P1" target="_top">spherical Hankel
  53         functions</a> of the first and second kind respectively:
  54       </p>
  55 <p>
  56         <span class="inlinemediaobject"><img src="../../../equations/hankel4.svg"></span>
  57       </p>
  58 <p>
  59         <span class="inlinemediaobject"><img src="../../../equations/hankel5.svg"></span>
  60       </p>
  61 <p>
  62         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
  63         type calculation rules</em></span></a> when T1 and T2 are different types.
  64         The functions are also optimised for the relatively common case that T1 is
  65         an integer.
  66       </p>
  67 <p>
  68         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
  69         be used to control the behaviour of the function: how it handles errors,
  70         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
  71         documentation for more details</a>.
  72       </p>
  73 <p>
  74         Note that while the arguments to these functions are real values, the results
  75         are complex. That means that the functions can only be instantiated on types
  76         <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>
  77         and <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
  78         The functions have also been extended to operate over the whole range of
  79         <span class="emphasis"><em>v</em></span> and <span class="emphasis"><em>x</em></span> (unlike <a class="link" href="../bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
  80         and <a class="link" href="../bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>).
  81       </p>
  82 <h5>
  83 <a name="math_toolkit.hankel.sph_hankel.h2"></a>
  84         <span class="phrase"><a name="math_toolkit.hankel.sph_hankel.testing"></a></span><a class="link" href="sph_hankel.html#math_toolkit.hankel.sph_hankel.testing">Testing</a>
  85       </h5>
  86 <p>
  87         There are just a few spot tests to exercise all the special case handling
  88         - the bulk of the testing is done on the Bessel functions upon which these
  89         are based.
  90       </p>
  91 <h5>
  92 <a name="math_toolkit.hankel.sph_hankel.h3"></a>
  93         <span class="phrase"><a name="math_toolkit.hankel.sph_hankel.accuracy"></a></span><a class="link" href="sph_hankel.html#math_toolkit.hankel.sph_hankel.accuracy">Accuracy</a>
  94       </h5>
  95 <p>
  96         Refer to <a class="link" href="../bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
  97         and <a class="link" href="../bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>.
  98       </p>
  99 <h5>
 100 <a name="math_toolkit.hankel.sph_hankel.h4"></a>
 101         <span class="phrase"><a name="math_toolkit.hankel.sph_hankel.implementation"></a></span><a class="link" href="sph_hankel.html#math_toolkit.hankel.sph_hankel.implementation">Implementation</a>
 102       </h5>
 103 <p>
 104         These functions are trivially implemented in terms of <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>
 105         and <a class="link" href="cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_2</a>.
 106       </p>
 107 </div>
 108 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 109 <td align="left"></td>
 110 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 111       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 112       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 113       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 114         Distributed under the Boost Software License, Version 1.0. (See accompanying
 115         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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