time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

lower_gamma_series.js (2060B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 *
     18 *
     19 * ## Notice
     20 *
     21 * The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_37_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
     22 *
     23 * ```text
     24 * (C) Copyright John Maddock 2006.
     25 * (C) Copyright Paul A. Bristow 2007.
     26 *
     27 * Use, modification and distribution are subject to the
     28 * Boost Software License, Version 1.0. (See accompanying file
     29 * LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
     30 * ```
     31 */
     32 
     33 'use strict';
     34 
     35 // MODULES //
     36 
     37 var sumSeries = require( './../../../../base/tools/sum-series' );
     38 var lowerIncompleteGammaSeries = require( './lower_incomplete_gamma_series.js' );
     39 
     40 
     41 // MAIN //
     42 
     43 /**
     44 * Sums elements of the series expansion of the lower incomplete gamma function.
     45 *
     46 * ## Method
     47 *
     48 * -   Multiply result by `((z^a) * (e^-z) / a)` to get the full lower incomplete integral.
     49 * -   Divide by `tgamma(a)` to get the normalized value.
     50 *
     51 * @private
     52 * @param {number} a - function parameter
     53 * @param {number} z - function parameter
     54 * @param {number} initialValue - initial value of the resulting sum
     55 * @returns {number} sum of terms of lower gamma series
     56 */
     57 function lowerGammaSeries( a, z, initialValue ) {
     58 	var result;
     59 	var s;
     60 
     61 	initialValue = initialValue || 0.0;
     62 	s = lowerIncompleteGammaSeries( a, z );
     63 	result = sumSeries( s, {
     64 		'initialValue': initialValue
     65 	});
     66 	return result;
     67 }
     68 
     69 
     70 // EXPORTS //
     71 
     72 module.exports = lowerGammaSeries;