What question did this study set out to answer?

The aim is to derive closed form formulas for a generalized double series using the Hurwitz-Lerch zeta function.

January 18, 2026Open Access

A note on a generalized double series

Key Points

The aim is to derive closed form formulas for a generalized double series using the Hurwitz-Lerch zeta function.
Employed contour integration for derivation.
Derived closed form formulae in terms of special functions.
Examined special cases of summation and product formulae.
Produced a table of quotient gamma functions and plot representations.
Identified closed form expressions involving the Hurwitz-Lerch zeta function.
Established relationships with trigonometric functions and the gamma function.
Provided visual aids (plots) and a comprehensive table for reader reference.

Abstract

By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special cases of the summation and product formulae in terms of the Hurwitz-Lerch zeta function, trigonometric functions and the gamma function. A short table of quotient gamma functions and plots are produced for easy reading by interested readers.

A note on a generalized double series

Key Points

Abstract

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