How to compute this integral involving sech? Does anybody know how to so solve this integral:
$$
\int\limits_{-\infty}^{+\infty}\text{sech}(t-h)\,e^{ikt/\epsilon}\,\mathrm{d}t
$$
and where $h\in \mathbb{R}$ is a constant, $k\in\mathbb{Z}$ and $\epsilon>0$.

A related problem. Here is another approach using the Mellin transform technique. First we write the integral as

$$ I = \int\limits_{-\infty}^{+\infty}\text{sech}(t-h)\,e^{ikt/\epsilon}\,\mathrm{d}t= e^{\frac{ik}{\epsilon}} \int\limits_{-\infty}^{+\infty}\text{sech}(t)\,e^{ikt/\epsilon}\,\mathrm{d}t= 2\,e^{\frac{ik}{\epsilon}} \int\limits_{-\infty}^{+\infty}\frac{e^{ikt/\epsilon}}{e^{t}+e^{-t}}\,\mathrm{d}t.  $$

To finish the problem follow the technique.
