On Closed Forms of Some Trigonometric Series

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.

Keywords

• Dirichlet <i>η</i>, <i>λ</i>, <i>β</i> functions
• Riemann’s zeta function
• Hurwitz’s zeta function
• harmonic numbers