correction.js (1636B)
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 'use strict'; 20 21 // MODULES // 22 23 var pow = require( '@stdlib/math/base/special/pow' ); 24 25 26 // VARIABLES // 27 28 var ONE_12 = 1.0 / 12.0; 29 var ONE_360 = 1.0 / 360.0; 30 var ONE_1260 = 1.0 / 1260.0; 31 32 33 // MAIN // 34 35 /** 36 * Returns a correction for Stirling's approximation. 37 * 38 * @private 39 * @param {NonNegativeInteger} k - input argument 40 * @returns {number} correction term 41 * 42 * @example 43 * var c = correction( 0 ); 44 * // returns 0.08106146679532726 45 */ 46 function correction( k ) { 47 var v; 48 switch ( k ) { 49 case 0: 50 return 0.08106146679532726; 51 case 1: 52 return 0.04134069595540929; 53 case 2: 54 return 0.02767792568499834; 55 case 3: 56 return 0.02079067210376509; 57 case 4: 58 return 0.01664469118982119; 59 case 5: 60 return 0.01387612882307075; 61 case 6: 62 return 0.01189670994589177; 63 case 7: 64 return 0.01041126526197209; 65 case 8: 66 return 0.009255462182712733; 67 case 9: 68 return 0.008330563433362871; 69 default: 70 k += 1; 71 v = pow( k, 2 ); 72 return (ONE_12 - ((ONE_360 - (ONE_1260/v)) / v)) / k; 73 } 74 } 75 76 77 // EXPORTS // 78 79 module.exports = correction;