# Laplace Transform Convergence

Cuthbert Nyack

The Laplace Transform F(s) of f(t) is defined as
The above integral does
not converge for functions that increase faster
than exponential and these functions do not have a Laplace
Transform. For many functions f(t) the integral and
hence the Laplace transform only converges
for some range of s. For thr Fourier transform to exist,
the region of convergence must include the imaginary axis.

Some examples of functions and the region
of convergence of the above integral are given below:-

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Copyright 1996 © Cuthbert A. Nyack.