Laplace Transform of Function of t minus a

Theorem
Let $\laptrans {\map f t} = \map F s$ denote the Laplace transform of $f$.

Let $f$ be a function such that $\laptrans f$ exists.

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

Then:


 * $\laptrans {\map f {t - a} } = e^{-a s} \map F s$

where $t > a$.

Also known as
This property of the Laplace transform operator is sometimes seen referred to as:
 * the second translation property

or:
 * the second shifting property.