Shows-that-1-ix-2-pi-xsinh-pix-with-z-0-t-z-1-e-t-dt-Then-Prove-that-0-1-ix-2-dx-pi-4-

Question Number 65786 by ~ À ® @ 237 ~ last updated on 04/Aug/19

S h o w s t h a t ∣ Γ (1 + i x) ∣^{2} = \frac{π}{x s i n h (π x)} w i t h Γ (z) = \int_{0_{}}^{\infty} t^{z - 1} e^{- t} d t

T h e n P r o v e t h a t \int_{0}^{\infty} ∣ Γ (1 + i x) ∣^{2} d x = \frac{π}{4}