Is it possible to have general formulae to calculate the discrete versions of "inverse laplace transform" ?
For example, do $F(s)=\sum\limits_{t=0}^\infty f(t)e^{-st}$ and $G(s)=\sum\limits_{t=0}^\infty g(t)e^{-st^2}$ admit solutions for $f(t)$, $g(t)$ ?