|
10
|
1 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
|
|
2
|
|
|
3
|
|
|
4
|
|
|
5
|
|
|
6
|
|
|
7
|
|
|
8
|
|
|
9
|
|
|
10
|
|
|
11
|
|
|
12
|
|
|
13 <html xmlns="http://www.w3.org/1999/xhtml">
|
|
|
14 <head>
|
|
|
15 <title>Math - The Commons Math User Guide - Special Functions</title>
|
|
|
16 <style type="text/css" media="all">
|
|
|
17 @import url("../css/maven-base.css");
|
|
|
18 @import url("../css/maven-theme.css");
|
|
|
19 @import url("../css/site.css");
|
|
|
20 </style>
|
|
|
21 <link rel="stylesheet" href="../css/print.css" type="text/css" media="print" />
|
|
|
22 <meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1" />
|
|
|
23 </head>
|
|
|
24 <body class="composite">
|
|
|
25 <div id="banner">
|
|
|
26 <span id="bannerLeft">
|
|
|
27
|
|
|
28 Commons Math User Guide
|
|
|
29
|
|
|
30 </span>
|
|
|
31 <div class="clear">
|
|
|
32 <hr/>
|
|
|
33 </div>
|
|
|
34 </div>
|
|
|
35 <div id="breadcrumbs">
|
|
|
36
|
|
|
37
|
|
|
38
|
|
|
39
|
|
|
40
|
|
|
41
|
|
|
42
|
|
|
43
|
|
|
44 <div class="xright">
|
|
|
45
|
|
|
46
|
|
|
47
|
|
|
48
|
|
|
49
|
|
|
50
|
|
|
51
|
|
|
52 </div>
|
|
|
53 <div class="clear">
|
|
|
54 <hr/>
|
|
|
55 </div>
|
|
|
56 </div>
|
|
|
57 <div id="leftColumn">
|
|
|
58 <div id="navcolumn">
|
|
|
59
|
|
|
60
|
|
|
61
|
|
|
62
|
|
|
63
|
|
|
64
|
|
|
65
|
|
|
66
|
|
|
67 <h5>User Guide</h5>
|
|
|
68 <ul>
|
|
|
69
|
|
|
70 <li class="none">
|
|
|
71 <a href="../userguide/index.html">Contents</a>
|
|
|
72 </li>
|
|
|
73
|
|
|
74 <li class="none">
|
|
|
75 <a href="../userguide/overview.html">Overview</a>
|
|
|
76 </li>
|
|
|
77
|
|
|
78 <li class="none">
|
|
|
79 <a href="../userguide/stat.html">Statistics</a>
|
|
|
80 </li>
|
|
|
81
|
|
|
82 <li class="none">
|
|
|
83 <a href="../userguide/random.html">Data Generation</a>
|
|
|
84 </li>
|
|
|
85
|
|
|
86 <li class="none">
|
|
|
87 <a href="../userguide/linear.html">Linear Algebra</a>
|
|
|
88 </li>
|
|
|
89
|
|
|
90 <li class="none">
|
|
|
91 <a href="../userguide/analysis.html">Numerical Analysis</a>
|
|
|
92 </li>
|
|
|
93
|
|
|
94 <li class="none">
|
|
|
95 <strong>Special Functions</strong>
|
|
|
96 </li>
|
|
|
97
|
|
|
98 <li class="none">
|
|
|
99 <a href="../userguide/utilities.html">Utilities</a>
|
|
|
100 </li>
|
|
|
101
|
|
|
102 <li class="none">
|
|
|
103 <a href="../userguide/complex.html">Complex Numbers</a>
|
|
|
104 </li>
|
|
|
105
|
|
|
106 <li class="none">
|
|
|
107 <a href="../userguide/distribution.html">Distributions</a>
|
|
|
108 </li>
|
|
|
109
|
|
|
110 <li class="none">
|
|
|
111 <a href="../userguide/fraction.html">Fractions</a>
|
|
|
112 </li>
|
|
|
113
|
|
|
114 <li class="none">
|
|
|
115 <a href="../userguide/transform.html">Transform Methods</a>
|
|
|
116 </li>
|
|
|
117
|
|
|
118 <li class="none">
|
|
|
119 <a href="../userguide/geometry.html">3D Geometry</a>
|
|
|
120 </li>
|
|
|
121
|
|
|
122 <li class="none">
|
|
|
123 <a href="../userguide/optimization.html">Optimization</a>
|
|
|
124 </li>
|
|
|
125
|
|
|
126 <li class="none">
|
|
|
127 <a href="../userguide/ode.html">Ordinary Differential Equations</a>
|
|
|
128 </li>
|
|
|
129
|
|
|
130 <li class="none">
|
|
|
131 <a href="../userguide/genetics.html">Genetic Algorithms</a>
|
|
|
132 </li>
|
|
|
133 </ul>
|
|
|
134 <a href="http://maven.apache.org/" title="Built by Maven" class="poweredBy">
|
|
|
135 <img alt="Built by Maven" src="../images/logos/maven-feather.png"></img>
|
|
|
136 </a>
|
|
|
137
|
|
|
138
|
|
|
139
|
|
|
140
|
|
|
141
|
|
|
142
|
|
|
143
|
|
|
144
|
|
|
145 </div>
|
|
|
146 </div>
|
|
|
147 <div id="bodyColumn">
|
|
|
148 <div id="contentBox">
|
|
|
149 <div class="section"><h2><a name="a5_Special_Functions"></a>5 Special Functions</h2>
|
|
|
150 <div class="section"><h3><a name="a5.1_Overview"></a>5.1 Overview</h3>
|
|
|
151 <p>
|
|
|
152 The special functions portion of Commons-Math contains several useful functions not
|
|
|
153 provided by <code>java.lang.Math</code>. These functions mostly serve as building blocks
|
|
|
154 for other portions of Commons-Math but, as others may find them useful as stand-alone
|
|
|
155 methods, these special functions were included as part of the Commons-Math public API.
|
|
|
156 </p>
|
|
|
157 </div>
|
|
|
158 <div class="section"><h3><a name="a5.2_Erf_functions"></a>5.2 Erf functions</h3>
|
|
|
159 <p><code>org.apache.commons.math.special.Erf</code> contains several useful functions involving the Error Function, Erf.
|
|
|
160 <table class="bodyTable"><tr class="a"><th>Function</th>
|
|
|
161 <th>Method</th>
|
|
|
162 <th>Reference</th>
|
|
|
163 </tr>
|
|
|
164 <tr class="b"><td>Error Function</td>
|
|
|
165 <td>erf</td>
|
|
|
166 <td>See <a href="http://mathworld.wolfram.com/Erf.html" class="externalLink">Erf</a> from MathWorld</td>
|
|
|
167 </tr>
|
|
|
168 </table>
|
|
|
169 </p>
|
|
|
170 </div>
|
|
|
171 <div class="section"><h3><a name="a5.3_Gamma_functions"></a>5.3 Gamma functions</h3>
|
|
|
172 <p><code>org.apache.commons.math.special.Gamma</code> contains several useful functions involving the Gamma Function.
|
|
|
173 <table class="bodyTable"><tr class="a"><th>Function</th>
|
|
|
174 <th>Method</th>
|
|
|
175 <th>Reference</th>
|
|
|
176 </tr>
|
|
|
177 <tr class="b"><td>Log Gamma</td>
|
|
|
178 <td>logGamma</td>
|
|
|
179 <td>See <a href="http://mathworld.wolfram.com/GammaFunction.html" class="externalLink">Gamma Function</a> from MathWorld</td>
|
|
|
180 </tr>
|
|
|
181 <tr class="a"><td>Regularized Gamma</td>
|
|
|
182 <td>regularizedGammaP</td>
|
|
|
183 <td>See <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html" class="externalLink">Regularized Gamma Function</a> from MathWorld</td>
|
|
|
184 </tr>
|
|
|
185 </table>
|
|
|
186 </p>
|
|
|
187 </div>
|
|
|
188 <div class="section"><h3><a name="a5.4_Beta_funtions"></a>5.4 Beta funtions</h3>
|
|
|
189 <p><code>org.apache.commons.math.special.Beta</code> contains several useful functions involving the Beta Function.
|
|
|
190 <table class="bodyTable"><tr class="b"><th>Function</th>
|
|
|
191 <th>Method</th>
|
|
|
192 <th>Reference</th>
|
|
|
193 </tr>
|
|
|
194 <tr class="a"><td>Log Beta</td>
|
|
|
195 <td>logBeta</td>
|
|
|
196 <td>See <a href="http://mathworld.wolfram.com/BetaFunction.html" class="externalLink">Beta Function</a> from MathWorld</td>
|
|
|
197 </tr>
|
|
|
198 <tr class="b"><td>Regularized Beta</td>
|
|
|
199 <td>regularizedBeta</td>
|
|
|
200 <td>See <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html" class="externalLink">Regularized Beta Function</a> from MathWorld</td>
|
|
|
201 </tr>
|
|
|
202 </table>
|
|
|
203 </p>
|
|
|
204 </div>
|
|
|
205 </div>
|
|
|
206
|
|
|
207 </div>
|
|
|
208 </div>
|
|
|
209 <div class="clear">
|
|
|
210 <hr/>
|
|
|
211 </div>
|
|
|
212 <div id="footer">
|
|
|
213 <div class="xright">©
|
|
|
214 2003-2010
|
|
|
215
|
|
|
216
|
|
|
217
|
|
|
218
|
|
|
219
|
|
|
220
|
|
|
221
|
|
|
222
|
|
|
223
|
|
|
224 </div>
|
|
|
225 <div class="clear">
|
|
|
226 <hr/>
|
|
|
227 </div>
|
|
|
228 </div>
|
|
|
229 </body>
|
|
|
230 </html>
|
