105 lines
1.9 KiB
Markdown
105 lines
1.9 KiB
Markdown
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---
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id: 5a23c84252665b21eecc7e76
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title: Gamma function
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challengeType: 5
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forumTopicId: 302271
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dashedName: gamma-function
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---
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# --description--
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Implement one algorithm (or more) to compute the [Gamma](https://en.wikipedia.org/wiki/Gamma function) ($\\Gamma$) function (in the real field only).
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The Gamma function can be defined as:
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<div style='padding-left: 4em;'><big><big>$\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt$</big></big></div>
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# --hints--
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`gamma` should be a function.
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```js
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assert(typeof gamma == 'function');
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```
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`gamma(.1)` should return a number.
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```js
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assert(typeof gamma(0.1) == 'number');
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```
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`gamma(.1)` should return `9.513507698668736`.
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```js
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assert.equal(round(gamma(0.1)), round(9.513507698668736));
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```
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`gamma(.2)` should return `4.590843711998803`.
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```js
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assert.equal(round(gamma(0.2)), round(4.590843711998803));
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```
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`gamma(.3)` should return `2.9915689876875904`.
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```js
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assert.equal(round(gamma(0.3)), round(2.9915689876875904));
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```
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`gamma(.4)` should return `2.218159543757687`.
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```js
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assert.equal(round(gamma(0.4)), round(2.218159543757687));
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```
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`gamma(.5)` should return `1.7724538509055159`.
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```js
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assert.equal(round(gamma(0.5)), round(1.7724538509055159));
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```
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# --seed--
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## --after-user-code--
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```js
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function round(x) {
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return Number(x).toPrecision(13);
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}
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```
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## --seed-contents--
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```js
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function gamma(x) {
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}
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```
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# --solutions--
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```js
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function gamma(x) {
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var p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
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771.32342877765313, -176.61502916214059, 12.507343278686905,
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-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
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];
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var g = 7;
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if (x < 0.5) {
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return Math.PI / (Math.sin(Math.PI * x) * gamma(1 - x));
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}
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x -= 1;
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var a = p[0];
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var t = x + g + 0.5;
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for (var i = 1; i < p.length; i++) {
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a += p[i] / (x + i);
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}
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var result=Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
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return result;
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}
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```
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