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.

The Lanczos approximation consists of the formula:

for the gamma function, with

The p coefficients are given by:

where C represents the (n, m)th element of the matrix of coefficients for the Chebyshev polynomials.

as equal to:

Log gamma is the following formula:

If a fixed g is chosen, the coefficients can be calculated in advance and the sum is recast into the following form:

Refer to Ag table.

Digamma is the following formula:

The multiplier of p is calculated from the following formula:

N = 1:

N = 2:

N = 3:

N > 3:

Refer to r table.

(Quote: wikipedia)