Evaluations of infinite series involving reciprocal hyperbolic functions

This paper presents a approach of summation of infinite series of hyperbolic functions. The approach is based on simple contour integral representions and residue computations with the help of some well known results of Eisenstein series given by Ramanujan and Berndt et al. Several series involving quadratic hyperbolic functions are evaluated, which can be expressed in terms of $z={}_2F_1(1/2,1/2;1;x)$ and $z'=dz/dx$. When a certain parameter in these series equal to $\pi$ the series are summable in terms of $\Gamma$ functions. Moreover, some interesting new consequences and illustrative examples are considered