---
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.
    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>.'')'

```

</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
  ];
   
  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);
  }
   
  var result=Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;

  return result;
}

```

</section>