How would I manage $\scr L \{e^{t^2}\}$? Does it even make sense to ask? Is it just a given that there are diverging Laplace functions that can't be handled?
2026-04-19 03:56:53.1776571013
What do you do if you need the Laplace transform of a diverging function?
902 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
It doesn't make sense. The domain of the Laplace transform is by definition the set of functions $f(t)$ for which $\int_0^\infty f(t)e^{-st}\,dt$ converges. (The set of all $s\in\mathbb{C}$ for which the integral converges is called the region of convergence of the transform.)
As such, the function you named simply is not in the domain of the Laplace transform operator.
It's like "needing" the integral of an function that is not integrable, or the derivative of a function that is not differentiable: oh well.