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let-0-lt-x-lt-1-and-x-0-t-x-1-e-t-dt-1-prove-that-x-1-x-pi-sin-pix-compliments-formulae-2-calculate-n-and-n-1-2-with-n-from-N-

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Question Number 42870 by maxmathsup by imad last updated on 03/Sep/18
let 0<x<1 and Γ(x) =∫_0 ^∞ t^(x−1) e^(−t) dt 1) prove that Γ(x).Γ(1−x) =(π/(sin(πx))) (compliments formulae) 2) calculate Γ(n) and Γ(n+(1/2)) with n from N.
let0<x<1andΓ(x)=∫0∞tx−1e−tdt1)provethatΓ(x).Γ(1−x)=πsin(πx)(complimentsformulae)2)calculateΓ(n)andΓ(n+12)withnfromN.

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