1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.numbers.gamma;
18
19 /**
20 * <a href="https://mathworld.wolfram.com/BetaFunction.html">Beta function</a>.
21 *
22 * <p>\[ B(a, b) = \frac{\Gamma(a)\ \Gamma(b)}{\Gamma(a+b)} = \frac{(a-1)!\ (b-1)!}{(a+b-1)!} \]
23 *
24 * <p>where \( \Gamma(z) \) is the gamma function.
25 *
26 * <p>This code has been adapted from the <a href="https://www.boost.org/">Boost</a>
27 * {@code c++} implementation {@code <boost/math/special_functions/beta.hpp>}.
28 *
29 * @see
30 * <a href="https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html">
31 * Boost C++ Beta function</a>
32 * @since 1.1
33 */
34 public final class Beta {
35
36 /** Private constructor. */
37 private Beta() {
38 // intentionally empty.
39 }
40
41 /**
42 * Computes the value of the
43 * <a href="https://mathworld.wolfram.com/BetaFunction.html">
44 * beta function</a> B(a, b).
45 *
46 * <p>\[ B(a, b) = \frac{\Gamma(a)\ \Gamma(b)}{\Gamma(a+b)} \]
47 *
48 * <p>where \( \Gamma(z) \) is the gamma function.
49 *
50 * @param a Parameter {@code a}.
51 * @param b Parameter {@code b}.
52 * @return the beta function \( B(a, b) \).
53 */
54 public static double value(double a,
55 double b) {
56 return BoostBeta.beta(a, b);
57 }
58 }