Fourier Series Of the Derivatives of Hurwitz and Lerch Zeta Functions

TL;DR

This paper derives Fourier series representations for Hurwitz and Lerch zeta functions and their derivatives, providing new insights into their harmonic analysis properties on the unit interval.

Contribution

It introduces explicit Fourier series formulas for Hurwitz and Lerch zeta functions and their derivatives, extending previous knowledge on their harmonic expansions.

Findings

Fourier series of Hurwitz zeta function derived

Fourier series of Lerch zeta function derived

Results based on Fourier coefficients and Parseval's theorem

Abstract

As a function of second variable, we identify the Fourier series of Hurwitz zeta function and its derivatives on the unit interval. Consequently, we obtain results based on the formula for Fourier coefficients and also on Parseval's theorem. We do likewise in the case of Lerch's zeta function and its derivatives.