2.4 KiB
2.4 KiB
title | id | challengeType | isHidden | forumTopicId |
---|---|---|---|---|
Gamma function | 5a23c84252665b21eecc7e76 | 5 | false | 302271 |
Description
$\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt$
Instructions
Tests
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))
Challenge Seed
function gamma(x) {
// Good luck!
}
After Test
function round(x) {
return Number(x).toPrecision(13);
}
Solution
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;
}