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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/gamma-function.md

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+---
+title: Gamma function
+id: 5a23c84252665b21eecc7e76
+challengeType: 5
+forumTopicId: 302271
+---
+
+## 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')
+  - text: <code>gamma(.1)</code> should return a number.
+    testString: assert(typeof gamma(.1)=='number')
+  - text: <code>gamma(.1)</code> should return <code>9.513507698668736</code>.
+    testString: assert.equal(round(gamma(.1)), round(9.513507698668736))
+  - text: <code>gamma(.2)</code> should return <code>4.590843711998803</code>.
+    testString: assert.equal(round(gamma(.2)), round(4.590843711998803))
+  - text: <code>gamma(.3)</code> should return <code>2.9915689876875904</code>.
+    testString: assert.equal(round(gamma(.3)), round(2.9915689876875904))
+  - text: <code>gamma(.4)</code> should return <code>2.218159543757687</code>.
+    testString: assert.equal(round(gamma(.4)), round(2.218159543757687))
+  - text: <code>gamma(.5)</code> should return <code>1.7724538509055159</code>.
+    testString: assert.equal(round(gamma(.5)), round(1.7724538509055159))
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function gamma(x) {
+
+}
+```
+
+</div>
+
+### After Test
+<div id='js-teardown'>
+
+```js
+function round(x) {
+  return Number(x).toPrecision(13);
+}
+```
+
+</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>