Mellin Transform of Dirac Delta Function

Theorem
Let $c \in \R_{>0}$ be a (strictly) positive real number.

Let $\map {\delta_c} t$ be the Dirac delta function.

Let $\MM$ be the Mellin transform.

Then:
 * $\map {\MM \set {\map {\delta_c} t} } s = c^{s - 1}$

Also see

 * Mellin Transform of Dirac Delta Function by Function