Gamma Function Abstract

The gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer, then Γ (n) = (n-1)! This functions as a basis to find a curve that connects the points (x, y) given by y = (x-1)! at the positive integer values for x. But this function is not restricted to whole numbers. A formula that allows the finding of the value of the Gamma function for any real value of n is as follows:

Γ (n+1) = ⌠∞

⌡0 e-x xn dx.