Exercise 4, § 2

Functions of a Real Variable, VII, 328

Let $t$ be a fixed real number $\neq 0$ ; show that as $s$ tends to $+\infty$

|\Gamma(-s + it)| \sim \sqrt{\frac{\pi}{2}} \left( s^{s+1/2} \ e^{-s} \ \sqrt{\sinh^2 \pi t + \sin^2 \pi s} \right)^j

(use the complements' relation).

Solution

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