Exercise 3, § 2

Functions of a Real Variable, VII, 328

Let $s$ be a fixed real number; show that when $t$ tends to $+\infty$ or to $-\infty$ one has

|\Gamma(s + it)| \sim \sqrt{2\pi} \ |t|^{s-1/2} \ e^{-(\pi/2)|t|}

and

\frac{\Gamma'(s + it)}{\Gamma(s + it)} \sim \log |t| .

Solution

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