  In this paper we study the Wiener-Hopf factorization for a class of L\'evy
processes with double-sided jumps, characterized by the fact that the density
of the L\'evy measure is given by an infinite series of exponential functions
with positive coefficients. We express the Wiener-Hopf factors as infinite
products over roots of a certain transcendental equation, and provide a series
representation for the distribution of the supremum/infimum process evaluated
at an independent exponential time. We also introduce five eight-parameter
families of L\'evy processes, defined by the fact that the density of the
L\'evy measure is a (fractional) derivative of the theta-function, and we show
that these processes can have a wide range of behavior of small jumps. These
families of processes are of particular interest for applications, since the
characteristic exponent has a simple expression, which allows efficient
numerical computation of the Wiener-Hopf factors and distributions of various
functionals of the process.
