0
$\begingroup$

Let $\epsilon > 0$, and $ n \in \mathbb{Z}^{+} $. Let $C_{n}$ be a positively oriented polygonal line that is from $-n + 1/2 - i \epsilon$ to $ 1/2 - i \epsilon$ and from $ 1/2 - i \epsilon$ to $ 1/2 + i \epsilon$ and from $ 1/2 + i \epsilon$ to $-n + 1/2 + i \epsilon$. And now define polygonal curve $C_{R}$ in the same way above but replacing $n$ with a real number $R>0$. Let $\Gamma$ be Gamma function. Then is it $$ \int_{C_{n}} \Gamma = \int_{C_{R}} \Gamma $$ as $n \to \infty$ ?

2 Answers 2