Zero Gamma?

Calculus Level 4

$\large \displaystyle \lim_{x \rightarrow 0^{-}} \Gamma(x)$

Find the value of the above limit.

-\infty

\infty

1 0

1 solution

Arghyadeep Chatterjee
Apr 28, 2020

We know $\large -\gamma = \lim_{x\to 0} (\Gamma(x) - \frac{1}{x})$

So we have $\large \lim_{x\to 0^{-}}(-\gamma + \frac{1}{x}) = \lim_{x\to 0^{-}} \Gamma(x)$

as $\gamma$ is finite and $\lim_{x\to 0^{-}}\frac{1}{x} \to -\infty$ .

we have $\large \lim_{x\to 0^{-}} \Gamma(x) \to -\infty$ .

Here $\gamma$ denotes the Euler Mascheroni constant .