Residue calculus for Laplace inversion

Summary

Residue calculus for Laplace inversion evaluates the Bromwich integral with the residue theorem. One closes the vertical line of integration with a large arc to the left. When $F$ decays on such arcs, the inverse Laplace transform is the sum of the residues of $e^{s t} F(s)$ at the poles of $F$. It turns inversion into a finite or infinite sum of explicit terms, one for each pole.