I found this problem and I have been trying to solve it without success. Find inverse Laplace transform of function $F:\mathbb{C} \to \mathbb{C}$ given as: $$F(s)=\frac{\coth(s)}{s^2}$$ using complex analysis. I tried solving this using residue which says that $$f(t)=\sum \text{Res} F(s) e^{(st)}$$ but I get that $s=0$ is pole of third order and it gets complicated and with much derivation. I know that I can use contour integration but again I have to solve this residue problem. I am wondering if there is any more elegant solution or if my way is the only way to solve this?
2026-03-30 01:47:02.1774835222
Inverse Laplace transform of $\frac{\coth(s)}{s^2}$
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