I have access to ordinary generating function $f$ which I can evaluate at $d$ arbitrary real-valued points $f(s_1),f(s_2),\ldots,f(s_d)$. I need to know the approximate value of $g(t_1)$, which is the exponential generating function $g$ evaluated at a single point $t_1>0$.
What's a practical way of doing this?
Wikipedia has a section on obtaining $g$ from $f$ using complex integration, but I think I need some kind of real-valued discrete transform.
Motivation: I need to go from Laplace domain to time domain, have efficient implementation of resolvent, but not a nice closed form.