Exponential and trigonometric sums associated with the Lerch zeta and Legendre chi functions

It was shown that numerous (known and new) results involving various special functions, such as the Hurwitz and Lerch zeta functions and Legendre chi function, could be established in a simple, general and unified manner. In this way, among others, we recovered the Wang and Williams–Zhang generalizations of the classical Eisenstein summation formula and obtained their previously unknown companion formulae.