I am trying to solve the inverse Laplace transform of the form \begin{equation} F(s) = \frac{s^{m}}{(1+a \cdot s)^{n}(1+b \cdot s)^{h}} \end{equation} where, $a$ and $b$ are known constants, $m$, $n$, and $h$ are all positive integers.
If $n$ and $h$ is known, then we might use the residue theorem to get the answer. However, in the case of this problem, $n$ and $h$ are unknown, which means that the higher order derivatives used for the residue theorem might be difficult to get.
Do you have any ideas on solving this problem. Thanks a lot in advane.