001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.numbers.gamma;
018
019/**
020 * <a href="https://mathworld.wolfram.com/BetaFunction.html">Beta function</a>.
021 *
022 * <p>\[ B(a, b) = \frac{\Gamma(a)\ \Gamma(b)}{\Gamma(a+b)} = \frac{(a-1)!\ (b-1)!}{(a+b-1)!} \]
023 *
024 * <p>where \( \Gamma(z) \) is the gamma function.
025 *
026 * <p>This code has been adapted from the <a href="https://www.boost.org/">Boost</a>
027 * {@code c++} implementation {@code <boost/math/special_functions/beta.hpp>}.
028 *
029 * @see
030 * <a href="https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/sf_beta/beta_function.html">
031 * Boost C++ Beta function</a>
032 * @since 1.1
033 */
034public final class Beta {
035
036    /** Private constructor. */
037    private Beta() {
038        // intentionally empty.
039    }
040
041    /**
042     * Computes the value of the
043     * <a href="https://mathworld.wolfram.com/BetaFunction.html">
044     * beta function</a> B(a, b).
045     *
046     * <p>\[ B(a, b) = \frac{\Gamma(a)\ \Gamma(b)}{\Gamma(a+b)} \]
047     *
048     * <p>where \( \Gamma(z) \) is the gamma function.
049     *
050     * @param a Parameter {@code a}.
051     * @param b Parameter {@code b}.
052     * @return the beta function \( B(a, b) \).
053     */
054    public static double value(double a,
055                               double b) {
056        return BoostBeta.beta(a, b);
057    }
058}