1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
|
/**
* @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 erfc = require( './../../../../base/special/erfc' );
var sqrt = require( './../../../../base/special/sqrt' );
var exp = require( './../../../../base/special/exp' );
var PI = require( '@stdlib/constants/float64/pi' );
// MAIN //
/**
* Calculates normalized Q when a is a half-integer.
*
* @private
* @param {number} a - function parameter
* @param {number} x - function parameter
* @returns {number} upper gamma fraction
*/
function finiteHalfGammaQ( a, x ) {
var half;
var term;
var sum;
var e;
var n;
e = erfc( sqrt(x) );
if ( e !== 0 && a > 1.0 ) {
term = exp( -x ) / sqrt( PI * x );
term *= x;
half = 0.5;
term /= half;
sum = term;
for ( n = 2; n < a; ++n ) {
term /= n - half;
term *= x;
sum += term;
}
e += sum;
}
return e;
}
// EXPORTS //
module.exports = finiteHalfGammaQ;
|
