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...

We will define the extension of q-Hurwitz zeta function due to Kim and Rim (2000) and study its properties. Finally, we lead to a useful new integral representation for the q-zeta function. 1. Introduction. Let 0 < q < 1 and for any positive integer k, define its q-analogue [k] q = (1 − q k)/(1 − q). Let C be the field of complex numbers. The q-zeta function due