# JavaScript: Calculate Lanczos approximation gamma

## JavaScript Math: Exercise-49 with Solution

Write a JavaScript function to calculate the Lanczos approximation gamma.

In mathematics, the Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the Gamma function with fixed precision.

Sample Solution:-

HTML Code:

``````<!DOCTYPE html>
<html>
<meta charset="utf-8">
<title>JavaScript function to calculate Lanczos approximation gamma</title>
<body>

</body>
</html>
```
```

JavaScript Code:

``````function Lanczos_Gamma(num)
{
var p = [
0.99999999999980993, 676.5203681218851, -1259.1392167224028,
771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
];
var i;
var g = 7;
if (num < 0.5) return Math.PI / (Math.sin(Math.PI * num) * calculus.LanczosGamma(1 - num));
num -= 1;
var a = p;
var t = num + g + 0.5;
for (i = 1; i < p.length; i++) {
a += p[i] / (num + i);
}
return Math.sqrt(2 * Math.PI) * Math.pow(t, num + 0.5) * Math.exp(-t) * a;
}
console.log(Lanczos_Gamma(5));
```
```

Sample Output:

```23.999999999999996
```

Flowchart: Live Demo:

See the Pen javascript-math-exercise-49 by w3resource (@w3resource) on CodePen.

Improve this sample solution and post your code through Disqus

What is the difficulty level of this exercise?

Test your Programming skills with w3resource's quiz.

﻿