eta.js (1517B)
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 isnan = require( './../../../../base/assert/is-nan' ); 24 var powm1 = require( './../../../../base/special/powm1' ); 25 var zeta = require( './../../../../base/special/riemann-zeta' ); 26 var LN2 = require( '@stdlib/constants/float64/ln-two' ); 27 28 29 // MAIN // 30 31 /** 32 * Evaluates the Dirichlet eta function. 33 * 34 * @param {number} s - input value 35 * @returns {number} function value 36 * 37 * @example 38 * var v = eta( 0.0 ); 39 * // returns 0.5 40 * 41 * @example 42 * var v = eta( -1.0 ); 43 * // returns 0.25 44 * 45 * @example 46 * var v = eta( 1.0 ); // => ln(2) 47 * // returns ~0.6931 48 * 49 * @example 50 * var v = eta( 3.14 ); 51 * // returns ~0.9096 52 * 53 * @example 54 * var v = eta( NaN ); 55 * // returns NaN 56 */ 57 function eta( s ) { 58 if ( isnan( s ) ) { 59 return NaN; 60 } 61 if ( s === 1.0 ) { 62 // Alternating harmonic series... 63 return LN2; 64 } 65 return -powm1( 2.0, 1.0-s ) * zeta( s ); 66 } 67 68 69 // EXPORTS // 70 71 module.exports = eta;