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# Gamma function

Calculation of the Gamma function using Lanczos approximation This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/4520/. Also, please do not modify any references to the original work (if any) contained in this content.

Gamma function is defined as

In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. In particular, for positive integer gamma function is

The main property of gamma function is its recurrence relation:

The Lanczos approximation is used to calculate Gamma function numerically. The Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964. You can check this link Lanczos approximation for details

Why is it needed? Wikipedia says:
Opening a random page in an advanced table of formulas, one may be as likely to spot the gamma function as a trigonometric function. One author describes the gamma function as "Arguably, the most common special function, or the least 'special' of them. The other transcendental functions listed below are called 'special' because you could conceivably avoid some of them by staying away from many specialized mathematical topics. On the other hand, the gamma function y = Γ(x) is most difficult to avoid."

Here it is needed because gamma function is part of distribution function formula for Student's distribution, which I need for next calculator. #### Gamma function

Digits after the decimal point: 2
Gamma function