Some identities with multi-generalized q -hyperharmonic numbers of order r

Abstract

The main purpose of this paper is to define multiple alternative q-harmonic numbers, H-n(k; q) and multi-generalized q-hyperharmonic numbers of order r, H-n(r) (k; q) by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms Li-q; k1,Li-k2,Li-...,Li-kd (t(1), t(2),...,t(d)) with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.