# 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:

JavaScript Code:

``````// Define a function named Lanczos_Gamma that calculates the Lanczos approximation of the gamma function for the given input 'num'.
function Lanczos_Gamma(num)
{
// Define the coefficients of the Lanczos approximation.
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;

// Check if the input is less than 0.5 and return the reciprocal identity if true.
if (num < 0.5) return Math.PI / (Math.sin(Math.PI * num) * calculus.LanczosGamma(1 - num));

num -= 1;

// Initialize 'a' and 't'.
var a = p[0];
var t = num + g + 0.5;

// Calculate the Lanczos approximation using the coefficients.
for (i = 1; i < p.length; i++) {
a += p[i] / (num + i);
}

// Return the result of the Lanczos approximation.
return Math.sqrt(2 * Math.PI) * Math.pow(t, num + 0.5) * Math.exp(-t) * a;
}

// Output the result of Lanczos_Gamma function with input 5.
console.log(Lanczos_Gamma(5));
```
```

Output:

```23.999999999999996
```

Flowchart:

Live Demo:

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

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