Some Evaluation of Infinite Series Involving Trigonometric and Hyperbolic Functions

Abstract

In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic functions. In particular, we evaluate in closed form certain classes of infinite series containing hyperbolic functions, which are related to Gamma functions and power of $$\pi $$ . Moreover, some interesting new consequences and illustrative examples are considered.