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 }