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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.
*/
'use strict';
// MODULES //
var pow = require( '@stdlib/math/base/special/pow' );
// VARIABLES //
var ONE_12 = 1.0 / 12.0;
var ONE_360 = 1.0 / 360.0;
var ONE_1260 = 1.0 / 1260.0;
// MAIN //
/**
* Returns a correction for Stirling's approximation.
*
* @private
* @param {NonNegativeInteger} k - input argument
* @returns {number} correction term
*
* @example
* var c = correction( 0 );
* // returns 0.08106146679532726
*/
function correction( k ) {
var v;
switch ( k ) {
case 0:
return 0.08106146679532726;
case 1:
return 0.04134069595540929;
case 2:
return 0.02767792568499834;
case 3:
return 0.02079067210376509;
case 4:
return 0.01664469118982119;
case 5:
return 0.01387612882307075;
case 6:
return 0.01189670994589177;
case 7:
return 0.01041126526197209;
case 8:
return 0.009255462182712733;
case 9:
return 0.008330563433362871;
default:
k += 1;
v = pow( k, 2 );
return (ONE_12 - ((ONE_360 - (ONE_1260/v)) / v)) / k;
}
}
// EXPORTS //
module.exports = correction;
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