Laplace Transform of Constant Mapping

Theorem
Let:


 * $f_c:\R \to \R$ or $\C$
 * $f_c \left({t}\right) = a$

be a constant mapping.

Let $\mathcal L$ be the Laplace Transform.

Then:


 * $\displaystyle \mathcal L \left\{ {f_c\left({t}\right)} \right\} = \frac a s$

for $\operatorname{Re}\left({s}\right) > a$.