prove-that-x-0-1-1-x-1-x-x-n-1-1-x-2-n-2-

Question Number 29842 by abdo imad last updated on 12/Feb/18

p r o v e t h a t \forall x \in] 0, 1 [\frac{1}{Γ (x) . Γ (1 - x)} = x \prod_{n = 1}^{\infty} (1 - \frac{x^{2}}{n^{2}}) .

Commented by abdo imad last updated on 12/Feb/18

y o u c a n u s e t h e p r o v e d f o r m u l a

Γ (x) = {l i m}_{n \to + \infty} \frac{n^{x} n!}{x (x + 1) \dots . (x + n)} .