  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
trigonometric functions. In particular, we evaluate in closed form certain
classes of infinite series containing hyperbolic trigonometric functions, which
are related to Gamma functions and \pi. Finally, some interesting new
consequences and illustrative examples are considered.
