Question: (Gamma Function) Let Î(n) = This integral converges by Problems 51 and 52. Show each of the following (note that the gamma function is defined

(Gamma Function) Let Î“(n) =

This integral converges by Problems 51 and 52. Show each of the following (note that the gamma function is defined for every positive real number n):
(a) Î“(1) = 1
(b) Î“ (n + 1) = n Î“(n)
(c) Î“(n + 1) = n!, if n is a positive integer?

x"-le dx,n>0.

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