The function defined by for x>0. Integration by parts yields Γ(x + 1) = xΓ(x), and Γ(1) = 1 so if n is a positive integer Γ(n) = (n−1)!.
Statistics
The gamma function, Γ, is defined by In general Γ(x+1) = xΓ(x). If x is a positive integer then Γ(x) = (x−1)! (seefactorial). If x is positive and an odd multiple of ½ then the value of Γ(x) is given by