--- /dev/null
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Spherical Harmonics</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.5.1">
+<link rel="up" href="../sf_poly.html" title="Polynomials">
+<link rel="prev" href="hermite.html" title="Hermite Polynomials">
+<link rel="next" href="../bessel.html" title="Bessel Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hermite.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+<div class="section">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.sf_poly.sph_harm"></a><a class="link" href="sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a>
+</h3></div></div></div>
+<h5>
+<a name="math_toolkit.sf_poly.sph_harm.h0"></a>
+ <span class="phrase"><a name="math_toolkit.sf_poly.sph_harm.synopsis"></a></span><a class="link" href="sph_harm.html#math_toolkit.sf_poly.sph_harm.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">spherical_harmonic</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="identifier">std</span><span class="special">::</span><span class="identifier">complex</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="special">></span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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="special">></span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><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="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. 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">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><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="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. 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">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. 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_poly.sph_harm.h1"></a>
+ <span class="phrase"><a name="math_toolkit.sf_poly.sph_harm.description"></a></span><a class="link" href="sph_harm.html#math_toolkit.sf_poly.sph_harm.description">Description</a>
+ </h5>
+<p>
+ 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
+ type calculation rules</em></span></a> when T1 and T2 are different types.
+ </p>
+<p>
+ The final <a class="link" href="../../policy.html" title="Chapter 15. 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 15. Policies: Controlling Precision, Error Handling etc">policy
+ documentation for more details</a>.
+ </p>
+<pre class="programlisting"><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="identifier">std</span><span class="special">::</span><span class="identifier">complex</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="special">></span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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="special">></span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+</pre>
+<p>
+ Returns the value of the Spherical Harmonic Y<sub>n</sub><sup>m</sup>(theta, phi):
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_0.svg"></span>
+ </p>
+<p>
+ The spherical harmonics Y<sub>n</sub><sup>m</sup>(theta, phi) are the angular portion of the solution
+ to Laplace's equation in spherical coordinates where azimuthal symmetry is
+ not present.
+ </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/src/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+ Care must be taken in correctly identifying the arguments to this function:
+ θ   is taken as the polar (colatitudinal) coordinate with θ   in [0, π], and φ   as
+ the azimuthal (longitudinal) coordinate with φ   in [0,2π). This is the convention
+ used in Physics, and matches the definition used by <a href="http://documents.wolfram.com/mathematica/functions/SphericalHarmonicY" target="_top">Mathematica
+ in the function SpericalHarmonicY</a>, but is opposite to the usual
+ mathematical conventions.
+ </p>
+<p>
+ Some other sources include an additional Condon-Shortley phase term of
+ (-1)<sup>m</sup> in the definition of this function: note however that our definition
+ of the associated Legendre polynomial already includes this term.
+ </p>
+<p>
+ This implementation returns zero for m > n
+ </p>
+<p>
+ For θ   outside [0, π] and φ   outside [0, 2π] this implementation follows the convention
+ used by Mathematica: the function is periodic with period π   in θ   and 2π   in φ.
+ Please note that this is not the behaviour one would get from a casual
+ application of the function's definition. Cautious users should keep θ   and
+ φ   to the range [0, π] and [0, 2π] respectively.
+ </p>
+<p>
+ See: <a href="http://mathworld.wolfram.com/SphericalHarmonic.html" target="_top">Weisstein,
+ Eric W. "Spherical Harmonic." From MathWorld--A Wolfram Web Resource</a>.
+ </p>
+</td></tr>
+</table></div>
+<pre class="programlisting"><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="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. 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">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+</pre>
+<p>
+ Returns the real part of Y<sub>n</sub><sup>m</sup>(theta, phi):
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_1.svg"></span>
+ </p>
+<pre class="programlisting"><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="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</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="Chapter 15. 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">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
+</pre>
+<p>
+ Returns the imaginary part of Y<sub>n</sub><sup>m</sup>(theta, phi):
+ </p>
+<p>
+ <span class="inlinemediaobject"><img src="../../../equations/spherical_2.svg"></span>
+ </p>
+<h5>
+<a name="math_toolkit.sf_poly.sph_harm.h2"></a>
+ <span class="phrase"><a name="math_toolkit.sf_poly.sph_harm.accuracy"></a></span><a class="link" href="sph_harm.html#math_toolkit.sf_poly.sph_harm.accuracy">Accuracy</a>
+ </h5>
+<p>
+ The following table shows peak errors for various domains of input arguments.
+ Note that only results for the widest floating point type on the system are
+ given as narrower types have <a class="link" href="../relative_error.html#math_toolkit.relative_error.zero_error">effectively
+ zero error</a>. Peak errors are the same for both the real and imaginary
+ parts, as the error is dominated by calculation of the associated Legendre
+ polynomials: especially near the roots of the associated Legendre function.
+ </p>
+<p>
+ All values are in units of epsilon.
+ </p>
+<div class="table">
+<a name="math_toolkit.sf_poly.sph_harm.table_spherical_harmonic_r"></a><p class="title"><b>Table 6.38. Error rates for spherical_harmonic_r</b></p>
+<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ </th>
+<th>
+ <p>
+ Microsoft Visual C++ version 12.0<br> Win32<br> double
+ </p>
+ </th>
+<th>
+ <p>
+ GNU C++ version 5.1.0<br> linux<br> double
+ </p>
+ </th>
+<th>
+ <p>
+ GNU C++ version 5.1.0<br> linux<br> long double
+ </p>
+ </th>
+<th>
+ <p>
+ Sun compiler version 0x5130<br> Sun Solaris<br> long double
+ </p>
+ </th>
+</tr></thead>
+<tbody><tr>
+<td>
+ <p>
+ Spherical Harmonics
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
+ </p>
+ </td>
+</tr></tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="math_toolkit.sf_poly.sph_harm.table_spherical_harmonic_i"></a><p class="title"><b>Table 6.39. Error rates for spherical_harmonic_i</b></p>
+<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ </th>
+<th>
+ <p>
+ Microsoft Visual C++ version 12.0<br> Win32<br> double
+ </p>
+ </th>
+<th>
+ <p>
+ GNU C++ version 5.1.0<br> linux<br> double
+ </p>
+ </th>
+<th>
+ <p>
+ GNU C++ version 5.1.0<br> linux<br> long double
+ </p>
+ </th>
+<th>
+ <p>
+ Sun compiler version 0x5130<br> Sun Solaris<br> long double
+ </p>
+ </th>
+</tr></thead>
+<tbody><tr>
+<td>
+ <p>
+ Spherical Harmonics
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
+ </p>
+ </td>
+</tr></tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+ Note that the worst errors occur when the degree increases, values greater
+ than ~120 are very unlikely to produce sensible results, especially when
+ the order is also large. Further the relative errors are likely to grow arbitrarily
+ large when the function is very close to a root.
+ </p>
+<h5>
+<a name="math_toolkit.sf_poly.sph_harm.h3"></a>
+ <span class="phrase"><a name="math_toolkit.sf_poly.sph_harm.testing"></a></span><a class="link" href="sph_harm.html#math_toolkit.sf_poly.sph_harm.testing">Testing</a>
+ </h5>
+<p>
+ A mixture of spot tests of values calculated using functions.wolfram.com,
+ and randomly generated test data are used: the test data was computed using
+ <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR</a> at 1000-bit
+ precision.
+ </p>
+<h5>
+<a name="math_toolkit.sf_poly.sph_harm.h4"></a>
+ <span class="phrase"><a name="math_toolkit.sf_poly.sph_harm.implementation"></a></span><a class="link" href="sph_harm.html#math_toolkit.sf_poly.sph_harm.implementation">Implementation</a>
+ </h5>
+<p>
+ These functions are implemented fairly naively using the formulae given above.
+ Some extra care is taken to prevent roundoff error when converting from polar
+ coordinates (so for example the <span class="emphasis"><em>1-x<sup>2</sup></em></span> term used by the
+ associated Legendre functions is calculated without roundoff error using
+ <span class="emphasis"><em>x = cos(theta)</em></span>, and <span class="emphasis"><em>1-x<sup>2</sup> = sin<sup>2</sup>(theta)</em></span>).
+ The limiting factor in the error rates for these functions is the need to
+ calculate values near the roots of the associated Legendre functions.
+ </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
+ Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
+ Holin, Bruno Lalande, John Maddock, Jeremy Murphy, 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
+ 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>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hermite.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>
projects / ceph.git / blobdiff