forked from johannesgerer/jburkardt-m
-
Notifications
You must be signed in to change notification settings - Fork 0
/
spherical_harmonic.html
198 lines (173 loc) · 4.97 KB
/
spherical_harmonic.html
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
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
<html>
<head>
<title>
SPHERICAL_HARMONIC - Evaluate Spherical Harmonic Functions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERICAL_HARMONIC <br> Evaluate Spherical Harmonic Functions
</h1>
<hr>
<p>
<b>SPHERICAL_HARMONIC</b>
is a MATLAB library which
evaluates spherical harmonic functions.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SPHERICAL_HARMONIC</b> is available in
<a href = "../../m_src/spherical_harmonic/spherical_harmonic.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
evaluates many special functions.
</p>
<p>
<a href = "../../m_src/polpak/polpak.html">
POLPAK</a>,
a MATLAB library which
evaluates a variety of mathematical functions.
</p>
<p>
<a href = "../../m_src/test_values/test_values.html">
TEST_VALUES</a>,
a MATLAB library which
contains some sample values of many mathematical functions.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Theodore Chihara,<br>
An Introduction to Orthogonal Polynomials,<br>
Gordon and Breach, 1978,<br>
ISBN: 0677041500,<br>
LC: QA404.5 C44.
</li>
<li>
Walter Gautschi,<br>
Orthogonal Polynomials: Computation and Approximation,<br>
Oxford, 2004,<br>
ISBN: 0-19-850672-4,<br>
LC: QA404.5 G3555.
</li>
<li>
Eric Weisstein,<br>
CRC Concise Encyclopedia of Mathematics,<br>
CRC Press, 2002,<br>
Second edition,<br>
ISBN: 1584883472,<br>
LC: QA5.W45
</li>
<li>
Stephen Wolfram,<br>
The Mathematica Book,<br>
Fourth Edition,<br>
Cambridge University Press, 1999,<br>
ISBN: 0-521-64314-7,<br>
LC: QA76.95.W65.
</li>
<li>
Shanjie Zhang, Jianming Jin,<br>
Computation of Special Functions,<br>
Wiley, 1996,<br>
ISBN: 0-471-11963-6,<br>
LC: QA351.C45.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "legendre_associated_normalized.m">
legendre_associated_normalized.m</a>,
evaluates the associated Legendre functions P(N,M)(X),
normalized for use in spherical harmonic calculations;
</li>
<li>
<a href = "legendre_associated_normalized_values.m">
legendre_associated_normalized_values.m</a>
returns values of the normalized associated Legendre functions.
</li>
<li>
<a href = "r8_factorial.m">r8_factorial.m</a>,
computes the (real) factorial function;
</li>
<li>
<a href = "spherical_harmonic.m">
spherical_harmonic.m</a>,
evaluates the spherical harmonic function;
</li>
<li>
<a href = "spherical_harmonic_values.m">
spherical_harmonic_values.m</a>,
returns some values of the spherical harmonic function;
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a timestamp;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "spherical_harmonic_test.m">spherical_harmonic_test.m</a>,
runs all the tests;
</li>
<li>
<a href = "spherical_harmonic_test_output.txt">spherical_harmonic_test_output.txt</a>,
is the output from the tests;
</li>
<li>
<a href = "spherical_harmonic_test01.m">spherical_harmonic_test01.m</a>,
tests LEGENDRE_ASSOCIATED_NORMALIZED.
</li>
<li>
<a href = "spherical_harmonic_test02.m">spherical_harmonic_test02.m</a>,
tests SPHERICAL_HARMONIC and SPHERICAL_HARMONIC_VALUES.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 18 May 2011.
</i>
<!-- John Burkardt -->
</body>
</html>