Laplace Transform of Function of t minus a

Theorem
Let $\mathcal L$ be the Laplace transform.

Let $f$ be a function such that $\mathcal L f$ exists.

Let $F \left({s}\right)$ be $\mathcal L \left\{ {f \left({t}\right)} \right\}$.

Let $a \in \C$ or $\R$ be constant.

Then:


 * $ \mathcal L \left\{ {f \left({t - a}\right)} \right\} = e^{-a s} F \left({s}\right)$

where $t > a$.