Gamma Lanczos Calculator Online

Explanation

The Lanczos approximation, developed by Cornelius Lanczos in 1964, is a technique for numerically computing the gamma function in mathematics. It is an efficient substitute for the more well-known Stirling's approximation for computing the gamma function with fixed accuracy/precision.
The lanczos approximation formula is given below.

for the gamma function, with

Here, g is a real constant that can be chosen arbitrarily under the constraint that Re(z+g+ 1/2) > 0. Calculating the coefficients p, which are g-dependent, is a little more challenging (see below). Although the formula presented here is only applicable to arguments in the right complex half-plane, the reflection formula allows it to be extended to the entire complex plane.

The convergent series A can be trimmed to produce an approximation with the required level of precision. The gamma function can be computed with conventional single or double floating-point precision using only about 5–10 terms of the series if an acceptable g (usually a small integer) is chosen. If a fixed g is selected, the coefficients may be determined beforehand, and the total is recast into the following form thanks to partial fraction decomposition:

Thus, computing the gamma function merely requires evaluating a few simple functions and multiplying the result by pre-stored constants. The GNU Scientific Library, Boost, CPython, and musl all use the Lanczos approximation, which was popularised by Numerical Recipes. According to this method, computing the gamma function is "not much more complex than other built-in methods/functions that we taken for granted, such as sin x or ex."

How to use Gamma Lanczos Calculator?

• You just need to enter the value of z in the input field.
• The result will automatically appear below.

More Calculation Examples (Gamma Lanczos Approximation)

• z: 23
• Γ(z+1) = 1.1240007277776E+21


• z: 6.8
• Γ(z+1) = 496.60607757369


• z: 9.12
• Γ(z+1) = 52173.084685486


• z: 17
• Γ(z+1) = 20922789888000