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Edouard DUPIN
2021-10-05 21:37:46 +02:00
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@@ -1,13 +1,13 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>TR1 C Functions Quick Reference</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../extern_c.html" title='Chapter&#160;7.&#160;TR1 and C99 external "C" Functions'>
<link rel="home" href="../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../extern_c.html" title='Chapter 9. TR1 and C99 external "C" Functions'>
<link rel="prev" href="c99.html" title="C99 C Functions">
<link rel="next" href="../root_finding.html" title="Chapter&#160;8.&#160;Root Finding &amp; Minimization Algorithms">
<link rel="next" href="../root_finding.html" title="Chapter 10. Root Finding &amp; Minimization Algorithms">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@@ -173,9 +173,10 @@
<p>
The assoc_laguerre functions return:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/laguerre_1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/laguerre_1.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for
the full template (header only) version of this function.
@@ -188,9 +189,10 @@
<p>
The assoc_legendre functions return:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/legendre_1b.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/legendre_1b.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for
the full template (header only) version of this function.
@@ -203,9 +205,10 @@
<p>
Returns the beta function of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/beta1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/beta1.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_beta/beta_function.html" title="Beta">beta</a> for
the full template (header only) version of this function.
@@ -218,9 +221,10 @@
<p>
Returns the complete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint6.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint6.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the
full template (header only) version of this function.
@@ -233,9 +237,10 @@
<p>
Returns the complete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint7.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint7.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the
full template (header only) version of this function.
@@ -249,9 +254,10 @@
Returns the complete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span>
and <span class="emphasis"><em>nu</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint8.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint8.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the
full template (header only) version of this function.
@@ -265,9 +271,10 @@
Returns the modified bessel function of the first kind of <span class="emphasis"><em>nu</em></span>
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/mbessel2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/mbessel2.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a> for
the full template (header only) version of this function.
@@ -281,9 +288,10 @@
Returns the bessel function of the first kind of <span class="emphasis"><em>nu</em></span> and
<span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/bessel2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/bessel2.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
for the full template (header only) version of this function.
@@ -297,9 +305,10 @@
Returns the modified bessel function of the second kind of <span class="emphasis"><em>nu</em></span>
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/mbessel3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/mbessel3.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a> for
the full template (header only) version of this function.
@@ -314,9 +323,10 @@
Returns the bessel function of the second kind (Neumann function) of <span class="emphasis"><em>nu</em></span>
and <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/bessel3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/bessel3.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
for the full template (header only) version of this function.
@@ -330,9 +340,10 @@
Returns the incomplete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>
and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint2.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the
full template (header only) version of this function.
@@ -346,9 +357,10 @@
Returns the incomplete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>
and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint3.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the
full template (header only) version of this function.
@@ -362,9 +374,10 @@
Returns the incomplete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span>,
<span class="emphasis"><em>nu</em></span> and <span class="emphasis"><em>phi</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/ellint4.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/ellint4.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the
full template (header only) version of this function.
@@ -377,9 +390,10 @@
<p>
Returns the exponential integral Ei of <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/expint_i_1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/expint_i_1.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="expint/expint_i.html" title="Exponential Integral Ei">expint</a> for the
full template (header only) version of this function.
@@ -392,9 +406,10 @@
<p>
Returns the n'th Hermite polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/hermite_0.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/hermite_0.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/hermite.html" title="Hermite Polynomials">hermite</a> for the
full template (header only) version of this function.
@@ -407,9 +422,10 @@
<p>
Returns the n'th Laguerre polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/laguerre_0.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/laguerre_0.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for
the full template (header only) version of this function.
@@ -422,9 +438,10 @@
<p>
Returns the l'th Legendre polynomial of <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/legendre_0.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/legendre_0.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for
the full template (header only) version of this function.
@@ -437,9 +454,10 @@
<p>
Returns the Riemann Zeta function of <span class="emphasis"><em>x</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/zeta1.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/zeta1.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="zetas/zeta.html" title="Riemann Zeta Function">zeta</a> for the full template
(header only) version of this function.
@@ -453,9 +471,10 @@
Returns the spherical Bessel function of the first kind of <span class="emphasis"><em>x</em></span>
j<sub>n</sub>(x):
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for
the full template (header only) version of this function.
@@ -469,9 +488,10 @@
Returns the spherical associated Legendre function of <span class="emphasis"><em>l</em></span>,
<span class="emphasis"><em>m</em></span> and <span class="emphasis"><em>theta</em></span>:
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/spherical_3.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/spherical_3.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic</a>
for the full template (header only) version of this function.
@@ -485,9 +505,10 @@
<p>
Returns the spherical Neumann function of <span class="emphasis"><em>x</em></span> y<sub>n</sub>(x):
</p>
<p>
<span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span>
</p></blockquote></div>
<p>
See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for
the full template (header only) version of this function.
@@ -521,11 +542,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, 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>