(Solution) - Gamma Function Let n This integral converges by Problems -(2025 Original AI-Free Solution)

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(Gamma Function) Let ?(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) ?(1) = 1
(b) ? (n + 1) = n ?(n)
(c) ?(n + 1) = n!, if n is a positive integer?