For example : For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler-Mascheroni constant ) : The n-th derivative of the gamma function is : The gamma function has simple poles at z = − n = 0 , − 1 , − 2 , − 3 , ... The residue there is Moreover , the gamma function has the following Laurent expansion in 1 valid for z − 1 ( 1 .
For example : For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler-Mascheroni constant ) : The n-th derivative of the gamma function is : Some particular values of the gamma function are : Gauss introduced the Pi function .