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/**
* @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/beta.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
*
* 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';

// MAIN //

/**
* Computes the delta in `beta(a,b,x) = prefix + delta * beta(a+k,b,x)`.
*
* ## Notes
*
* Specifically, the function calculates
*
* ```tex
* \frac{ (a)(a+1)(a+2)...(a+k-1) }{ (b)(b+1)(b+2)...(b+k-1) }
* ```
*
* The function should only called with small `k`; for large `k`, it is grossly inefficient.
*
* @private
* @param {number} a - input value
* @param {number} b - input value
* @param {NonNegativeInteger} k - input value
* @returns {number} ratio value
*/
function risingFactorialRatio( a, b, k ) {
	var result;
	var i;
	if ( k === 0 ) {
		return 1.0;
	}
	result = 1.0;
	for ( i = 0; i < k; i++ ) {
		result *= ( a + i ) / ( b + i );
	}
	return result;
}


// EXPORTS //

module.exports = risingFactorialRatio;
