Mellin Transform of Heaviside Step Function

Theorem
Let $c$ be a constant real number.

Let $u_c \left({t}\right)$ be the Heaviside step function.

Let $\mathcal M$ be the Mellin transform.

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

for $c > 0, \Re \left({s}\right) < 0$.