Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...

The history of problems of evaluation of series associated with the Riemann Zeta function can be traced back to Christian Goldbach (1690–1764) and Leonhard Euler (1707–1783). Many di¤erent techniques to evaluate various series involving the Zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Zeta function can be eval...

Abstract. In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher’s identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting formulas related to values of the Hurwitz zeta function. We also get an extension of the bivariate identity of Cohen to values of the Hurwitz zeta fu...