F$\displaystyle \left(\vphantom{ s}\right.$s$\displaystyle \left.\vphantom{ s}\right)$ = L$\displaystyle \left\{\vphantom{ f}\right.$f$\displaystyle \left.\vphantom{ f}\right\}$$\displaystyle \left(\vphantom{ s}\right.$s$\displaystyle \left.\vphantom{ s}\right)$ = $\displaystyle \int_{{0}}^{{\infty
}}$e-stf (t)dt