Manuals/calci/GAMMAFUNCTION

GAMMAFUNCTION (z)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z} is any positive real number.

Description

This function gives the value of the Gamma function.
The Gamma function is defined to be an extension of the factorial to complex and real number arguments.
That is, if n is a positive integer:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma (n)=(n-1)!}

Gamma function is defined for all complex numbers except the non-positive integers.
For complex numbers with a positive real part, it is defined via a convergent improper integral:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma (z) = \int\limits_{0}^{\infty} x^{z-1} e^{-x} dx }