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---
title: Gamma function
id: 5a23c84252665b21eecc7e76
challengeType: 5
---
## Description
< section id = 'description' >
Implement one algorithm (or more) to compute the < a href = "https://en.wikipedia.org/wiki/Gamma function" > Gamma</ a > ($\Gamma$) function (in the real field only).
The Gamma function can be defined as:
< div style = 'padding-left: 4em;' >< big >< big > $\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt$</ big ></ big ></ div >
< / section >
## Instructions
< section id = 'instructions' >
< / section >
## Tests
< section id = 'tests' >
```yml
tests:
- text: < code > gamma</ code > should be a function.
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testString: 'assert(typeof gamma=="function","< code > gamma< / code > should be a function.")'
- text: '< code > gamma("+tests[0]+")</ code > should return a number.'
testString: 'assert(typeof gamma(tests[0])=="number","< code > gamma("+tests[0]+")< / code > should return a number.")'
- text: '< code > gamma("+tests[0]+")</ code > should return < code > "+results[0]+"</ code > .'
testString: 'assert.equal(gamma(tests[0]),results[0],"< code > gamma("+tests[0]+")< / code > should return < code > "+results[0]+"< / code > .")'
- text: '< code > gamma("+tests[1]+")</ code > should return < code > "+results[1]+"</ code > .'
testString: 'assert.equal(gamma(tests[1]),results[1],"< code > gamma("+tests[1]+")< / code > should return < code > "+results[1]+"< / code > .")'
- text: '< code > gamma("+tests[2]+")</ code > should return < code > "+results[2]+"</ code > .'
testString: 'assert.equal(gamma(tests[2]),results[2],"< code > gamma("+tests[2]+")< / code > should return < code > "+results[2]+"< / code > .")'
- text: '< code > gamma("+tests[3]+")</ code > should return < code > "+results[3]+"</ code > .'
testString: 'assert.equal(gamma(tests[3]),results[3],"< code > gamma("+tests[3]+")< / code > should return < code > "+results[3]+"< / code > .")'
- text: '< code > gamma("+tests[4]+")</ code > should return < code > "+results[4]+"</ code > .'
testString: 'assert.equal(gamma(tests[4]),results[4],"< code > gamma("+tests[4]+")< / code > should return < code > "+results[4]+"< / code > .")'
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function gamma (x) {
// Good luck!
}
```
< / div >
### After Test
< div id = 'js-teardown' >
```js
console.info('after the test');
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
function gamma(x) {
var p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
771.32342877765313, -176.61502916214059, 12.507343278686905,
-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
];
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var g = 7;
if (x < 0.5 ) {
return Math.PI / (Math.sin(Math.PI * x) * gamma(1 - x));
}
x -= 1;
var a = p[0];
var t = x + g + 0.5;
for (var i = 1; i < p.length ; i + + ) {
a += p[i] / (x + i);
}
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var result=Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
return result;
}
```
< / section >