let-give-x-0-t-x-1-e-t-dt-and-x-gt-0-gamma-euler-function-prove-that-x-lim-n-gt-n-n-x-n-n-1-n-2-n-x-

Question Number 26564 by abdo imad last updated on 26/Dec/17

l e t g i v e Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t a n d x > 0 (g a m m a e u l e r f u n c t i o n)

p r o v e t h a t Γ (x) = {l i m}_{n - >\propto} \frac{(n!) n^{x}}{n (n + 1) (n + 2) \dots (n + x)}