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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
and . When a certain parameter in these
series equal to the series are summable in terms of functions.
Moreover, some interesting new consequences and illustrative examples are
considered
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