1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".
(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library – Reference Manual: Conical Functions</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Conical Functions">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Conical Functions">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Legendre-Functions-and-Spherical-Harmonics.html#Legendre-Functions-and-Spherical-Harmonics" rel="up" title="Legendre Functions and Spherical Harmonics">
<link href="Radial-Functions-for-Hyperbolic-Space.html#Radial-Functions-for-Hyperbolic-Space" rel="next" title="Radial Functions for Hyperbolic Space">
<link href="Associated-Legendre-Polynomials-and-Spherical-Harmonics.html#Associated-Legendre-Polynomials-and-Spherical-Harmonics" rel="previous" title="Associated Legendre Polynomials and Spherical Harmonics">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Conical-Functions"></a>
<div class="header">
<p>
Next: <a href="Radial-Functions-for-Hyperbolic-Space.html#Radial-Functions-for-Hyperbolic-Space" accesskey="n" rel="next">Radial Functions for Hyperbolic Space</a>, Previous: <a href="Associated-Legendre-Polynomials-and-Spherical-Harmonics.html#Associated-Legendre-Polynomials-and-Spherical-Harmonics" accesskey="p" rel="previous">Associated Legendre Polynomials and Spherical Harmonics</a>, Up: <a href="Legendre-Functions-and-Spherical-Harmonics.html#Legendre-Functions-and-Spherical-Harmonics" accesskey="u" rel="up">Legendre Functions and Spherical Harmonics</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Conical-Functions-1"></a>
<h4 class="subsection">7.24.3 Conical Functions</h4>
<p>The Conical Functions <em>P^\mu_{-(1/2)+i\lambda}(x)</em> and <em>Q^\mu_{-(1/2)+i\lambda}</em>
are described in Abramowitz & Stegun, Section 8.12.
</p>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fhalf"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_half</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fhalf_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_half_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular Spherical Conical Function
<em>P^{1/2}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fmhalf"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_mhalf</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fmhalf_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_mhalf_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular Spherical Conical Function
<em>P^{-1/2}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005f0"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_0</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005f0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_0_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the conical function
<em>P^0_{-1/2 + i \lambda}(x)</em>
for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005f1"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_1</strong> <em>(double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005f1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_1_e</strong> <em>(double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the conical function
<em>P^1_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_sph_reg</strong> <em>(int <var>l</var>, double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fsph_005freg_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_sph_reg_e</strong> <em>(int <var>l</var>, double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Regular Spherical Conical Function
<em>P^{-1/2-l}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>, <em>l >= -1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg"></a>Function: <em>double</em> <strong>gsl_sf_conicalP_cyl_reg</strong> <em>(int <var>m</var>, double <var>lambda</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fconicalP_005fcyl_005freg_005fe"></a>Function: <em>int</em> <strong>gsl_sf_conicalP_cyl_reg_e</strong> <em>(int <var>m</var>, double <var>lambda</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the Regular Cylindrical Conical Function
<em>P^{-m}_{-1/2 + i \lambda}(x)</em> for <em>x > -1</em>, <em>m >= -1</em>.
</p></dd></dl>
</body>
</html>
|
