JavaScript: Calculate Lanczos approximation gamma

Last update on April 22 2023 12:19:34 (UTC/GMT +8 hours)

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>
<head>
  <meta charset="utf-8">
  <title>JavaScript function to calculate Lanczos approximation gamma</title>
</head>
<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[0];
  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:

$Flowchart: JavaScript Math - Calculate Lanczos approximation gamma$

Live Demo:

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

Improve this sample solution and post your code through Disqus

Previous: Write a JavaScript function to calculate the falling factorial of a number.
Next: Write a JavaScript program to add two complex numbers.