On closed forms of some trigonometric series

Slobodan B. Tričković, Miomir S. Stanković

Published 2024-07-16Version 1

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.