On closed forms of some trigonometric series

TL;DR

This paper derives new closed-form formulas for certain trigonometric series that involve singularities, using the Choi-Srivastava theorem to express them in terms of Hurwitz zeta function derivatives.

Contribution

It introduces alternative closed-form expressions for specific trigonometric series with singular parameters, expanding the mathematical tools available for such series.

Findings

Closed-form formulas for sine and cosine series with singular parameters.

Use of Choi-Srivastava theorem to relate series to Hurwitz zeta function derivatives.

Enhanced understanding of trigonometric series in mathematical analysis.

Abstract

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi-Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz's zeta function derivative.