Prove-that-for-m-0-1-2-3-lim-x-m-x-

Question Number 2434 by Yozzi last updated on 20/Nov/15

P r o v e t h a t f o r m = 0, 1, 2, 3, \dots

\lim_{x \to - m} Γ (x) = \infty .

Answered by 123456 last updated on 25/Nov/15

Γ (x + 1) = x Γ (x)

so

Γ (x) = \frac{Γ (x + 1)}{x}

Γ (x - 1) = \frac{Γ (x)}{x - 1}

with this we can undestand why

gamma function have simply poles

at x \in Z_{-} \cup {0}

however if you plot the gamma function

\lim_{x \to 0} Γ (x) = ∄

because

\lim_{x \to 0^{+}} Γ (x) = + \infty

\lim_{x \to 0^{-}} Γ (x) = - \infty

similiar things hold for the remaining

Commented by prakash jain last updated on 25/Nov/15

Γ (0)