Prove-that-the-Euler-Constant-is-qlso-equal-to-lim-x-1-x-1-x-x-1-

Question Number 117826 by snipers237 last updated on 13/Oct/20

P r o v e t h a t t h e E u l e r C o n s t a n t i s q l s o e q u a l t o

\lim_{x \to - 1} Γ (x) - \frac{1}{x (x + 1)}

Answered by mnjuly1970 last updated on 14/Oct/20

s o l u t i o n ::

{l i m}_{x \to - 1} [Γ (x) - \frac{1}{x (x + 1)}]

= {l i m}_{x \to - 1} (\frac{Γ (x + 2) - 1}{x (x + 1)})

\overset{l^{'} h o s p i t a l}{=} {l i m}_{x \to - 1} (\frac{Γ^{'} (x + 2)}{2 x + 1})

= \frac{Γ^{'} (1)}{- 1} = - Γ^{'} (1) = - ψ (1) Γ (1) = γ

w h e r e :: γ i s E u l e r -

M a s h e r o n i c o n s t a n t

\dots m . n . 1970 \dots