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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
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Mellin transform of powers of gamma function
If $a>0$, the Cahen-Mellin integral gives
$$\DeclareMathOperator{\Res}{\operatorname{Res}}
\frac{1}{2\pi i}\int\limits_{a-i\infty}^{a+i \infty}\varGamma(z) u^{-z}dz=e^{-u}=\sum\limits_{m=0}^{\infty}\ …