Table of Integrals, Series, and Products, 8th Edition

12

Fourier, Laplace, and Mellin Transforms

12.1–12.4 Integral Transforms

12.11 Laplace transform

The Laplace transform of the function $f(x)$, denoted by $F(s)$, is defined by the integral

$F(s)={\displaystyle {\int }_0^{\infty }f\left(x\right)e^{-sx}\text{d}x,}\text{Re}s>0$

The functions $f(x)$ and $F(s)$