Acceleration and Generalization of Some infinite Series

In this paper, we give new series representation for well-known mathematical constant such as, Catalan Constant and alternating series of the),;,(dcbaK[4]. Moreover, give new series representation Lerch Zeta function and its generalizations H-Lerch Zeta function and G-LerchZeta function. We also provide the convergence of series and some special case of it. Moreover, its relations with other mathematical functions like Riemann Zeta function, Poly-logarithm function, Dirichlet beta function etc. All the series we have found provide quite useful analytic approximation.