Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions

Peng-Cheng Hang, Alexey Kuznetsov

We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $\sinh (\ddot{I}€x)$ or $\cosh (\ddot{I}€x)$. In many cases, the resulting Fourie…