Question

For s > 0 define the gamma function I (s) by T () = [co-dt. Show that I (8) extends to an analytic function in the half-plane 20 = {ZEC: Rez >0}, and that the above formula continues to hold there. Hint: Show that S T. (s) ds = 0 for every triangle T in C where I (8) = le-+48-1dt for S E C and 0 <€ < 1.

Answer 1

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