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

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7e76	Gamma function	5	302271	gamma-function

--description--

Implement one algorithm (or more) to compute the Gamma (\\Gamma) function (in the real field only).

The Gamma function can be defined as:

$\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt$

--hints--

gamma should be a function.

assert(typeof gamma == 'function');

gamma(.1) should return a number.

assert(typeof gamma(0.1) == 'number');

gamma(.1) should return 9.513507698668736.

assert.equal(round(gamma(0.1)), round(9.513507698668736));

gamma(.2) should return 4.590843711998803.

assert.equal(round(gamma(0.2)), round(4.590843711998803));

gamma(.3) should return 2.9915689876875904.

assert.equal(round(gamma(0.3)), round(2.9915689876875904));

gamma(.4) should return 2.218159543757687.

assert.equal(round(gamma(0.4)), round(2.218159543757687));

gamma(.5) should return 1.7724538509055159.

assert.equal(round(gamma(0.5)), round(1.7724538509055159));

--seed--

--after-user-code--

function round(x) {
  return Number(x).toPrecision(13);
}

--seed-contents--

function gamma(x) {

}

--solutions--

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;
}