Mellin Transform of Heaviside Step Function

Theorem
Let $c$ be a constant real number.

Let $\map {u_c} t$ be the Heaviside step function.

Let $\MM$ be the Mellin transform.

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

for $c > 0, \map \Re s < 0$.