Generalized Series of Bernoulli Type

The problem of evaluating an infinite series whose successive terms are reciprocal squares the natural numbers was posed without a solution being offered in middle seventeenth century. In modern era, it is part theory Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve by considering other more tractable which were superficially similar and he hoped could be algebraically manipulated yield difficult series. This approach eventually unsuccessful, however, did produce early monograph on summation It remained for Bernoulli’s student countryman Leonhard Euler ultimately determine sum . We characterize class based generalizing original work adding two additional parameters summations. also develop recursion formula that allows any member