@stdlib/math-base-special-gammainc/lib/lower_gamma_series.js

Incomplete gamma function.

/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* 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.
*
* ```text
* (C) Copyright John Maddock 2006.
* (C) Copyright Paul A. Bristow 2007.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/

'use strict';

// MODULES //

var sumSeries = require( '@stdlib/math-base-tools-sum-series' );
var lowerIncompleteGammaSeries = require( './lower_incomplete_gamma_series.js' );


// MAIN //

/**
* Sums elements of the series expansion of the lower incomplete gamma function.
*
* ## Method
*
* -   Multiply result by `((z^a) * (e^-z) / a)` to get the full lower incomplete integral.
* -   Divide by `tgamma(a)` to get the normalized value.
*
* @private
* @param {number} a - function parameter
* @param {number} z - function parameter
* @param {number} initialValue - initial value of the resulting sum
* @returns {number} sum of terms of lower gamma series
*/
function lowerGammaSeries( a, z, initialValue ) {
	var result;
	var s;

	initialValue = initialValue || 0.0;
	s = lowerIncompleteGammaSeries( a, z );
	result = sumSeries( s, {
		'initialValue': initialValue
	});
	return result;
}


// EXPORTS //

module.exports = lowerGammaSeries;