Mellin Transform of Exponential

Theorem
Let $a$ be a complex constant and $e^t$ be the complex exponential.

Let $\MM$ be the Mellin transform.

Then:
 * $\map {\MM \set {e^{-a t} } } s = a^{-s} \, \map \Gamma s$

where $\map \Re a, \map \Re s > 0$

Also see

 * Mellin Transform of Higher Order Exponential