1 |
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2 | import { isInteger } from '../../utils/number.js';
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3 | import { product } from '../../utils/product.js';
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4 | export function gammaNumber(n) {
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5 | var x;
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6 |
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7 | if (isInteger(n)) {
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8 | if (n <= 0) {
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9 | return isFinite(n) ? Infinity : NaN;
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10 | }
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11 |
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12 | if (n > 171) {
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13 | return Infinity;
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14 | }
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15 |
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16 | return product(1, n - 1);
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17 | }
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18 |
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19 | if (n < 0.5) {
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20 | return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n));
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21 | }
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22 |
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23 | if (n >= 171.35) {
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24 | return Infinity;
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25 | }
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26 |
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27 | if (n > 85.0) {
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28 |
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29 | var twoN = n * n;
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30 | var threeN = twoN * n;
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31 | var fourN = threeN * n;
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32 | var fiveN = fourN * n;
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33 | return Math.sqrt(2 * Math.PI / n) * Math.pow(n / Math.E, n) * (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) - 571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) + 5246819 / (75246796800 * fiveN * n));
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34 | }
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35 |
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36 | --n;
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37 | x = gammaP[0];
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38 |
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39 | for (var i = 1; i < gammaP.length; ++i) {
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40 | x += gammaP[i] / (n + i);
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41 | }
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42 |
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43 | var t = n + gammaG + 0.5;
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44 | return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x;
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45 | }
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46 | gammaNumber.signature = 'number';
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47 |
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48 | export var gammaG = 4.7421875;
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49 | export var gammaP = [0.99999999999999709182, 57.156235665862923517, -59.597960355475491248, 14.136097974741747174, -0.49191381609762019978, 0.33994649984811888699e-4, 0.46523628927048575665e-4, -0.98374475304879564677e-4, 0.15808870322491248884e-3, -0.21026444172410488319e-3, 0.21743961811521264320e-3, -0.16431810653676389022e-3, 0.84418223983852743293e-4, -0.26190838401581408670e-4, 0.36899182659531622704e-5]; |
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