100 lines
3.0 KiB
Markdown
100 lines
3.0 KiB
Markdown
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---
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title: Gamma function
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id: 5a23c84252665b21eecc7e76
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localeTitle: 5a23c84252665b21eecc7e76
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challengeType: 5
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---
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## Description
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<section id='description'>
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Implemente un algoritmo (o más) para calcular la función <a href="https://en.wikipedia.org/wiki/Gamma function">Gamma</a> ($ \ Gamma $) (solo en el campo real).
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La función Gamma se puede definir como:
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<div style='padding-left: 4em;'> <big><big>$ \ Gamma (x) = \ displaystyle \ int_0 ^ \ infty t ^ {x-1} e ^ {- t} dt $</big></big> </div>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>gamma</code> debe ser una función.
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testString: 'assert(typeof gamma=="function","<code>gamma</code> should be a function.")'
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- text: ' <code>gamma("+tests[0]+")</code> debe devolver un número.'
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testString: 'assert(typeof gamma(tests[0])=="number","<code>gamma("+tests[0]+")</code> should return a number.")'
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- text: ' <code>gamma("+tests[0]+")</code> debe devolver <code>"+results[0]+"</code> .'
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testString: 'assert.equal(gamma(tests[0]),results[0],"<code>gamma("+tests[0]+")</code> should return <code>"+results[0]+"</code>.")'
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- text: ' <code>gamma("+tests[1]+")</code> debe devolver <code>"+results[1]+"</code> .'
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testString: 'assert.equal(gamma(tests[1]),results[1],"<code>gamma("+tests[1]+")</code> should return <code>"+results[1]+"</code>.")'
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- text: ' <code>gamma("+tests[2]+")</code> debe devolver <code>"+results[2]+"</code> .'
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testString: 'assert.equal(gamma(tests[2]),results[2],"<code>gamma("+tests[2]+")</code> should return <code>"+results[2]+"</code>.")'
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- text: ' <code>gamma("+tests[3]+")</code> debe devolver <code>"+results[3]+"</code> .'
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testString: 'assert.equal(gamma(tests[3]),results[3],"<code>gamma("+tests[3]+")</code> should return <code>"+results[3]+"</code>.")'
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- text: ' <code>gamma("+tests[4]+")</code> debe devolver <code>"+results[4]+"</code> .'
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testString: 'assert.equal(gamma(tests[4]),results[4],"<code>gamma("+tests[4]+")</code> should return <code>"+results[4]+"</code>.")'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function gamma (x) {
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// Good luck!
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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