Mellin Transform of Dirac Delta Function

Theorem
Let $\delta \left({t}\right)$ be the Dirac delta function.

Let $c$ be a positive real number.

Let $\mathcal M$ be the Mellin transform.

Then:
 * $\mathcal M \left\{ { \delta_c \left({t}\right)} \right\} \left({s}\right) = c^{s-1}$

Also see

 * Mellin Transform of Dirac Delta Function by Function