Inverse Laplace transform of $\exp(-1/\sqrt{s})$ I'm looking for the inverse Laplace transform of:
$$F(s) = \exp(-1/\sqrt{s}).$$
Does the inverse Laplace transform exist? Do you have a reference in which this transform is given?

Shouldn't the answer be, "Does not exist?"  That is because, for inverse Laplace Transform to exist it is necessary that, $\lim\limits_{s\rightarrow \infty} F(s) = 0$.  Here, clearly $\lim\limits_{s\rightarrow \infty}e^{-\frac{1}{\sqrt{s}}} = 1 \neq 0$.
