Manuals/calci/GAMMAFUNCTION

GAMMAFUNCTION (z)

• $z$ 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:

$\Gamma (n)=(n-1)!$

• 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:

$\Gamma (z)=\int \limits _{0}^{\infty }x^{z-1}e^{-x}dx$