Symmetry, Vol. 15, Pages 917: Some Identities with Multi-Generalized q-Hyperharmonic Numbers of Order r

Symmetry, Vol. 15, Pages 917: Some Identities with Multi-Generalized q-Hyperharmonic Numbers of Order r

Symmetry doi: 10.3390/sym15040917

Authors: Zhihua Chen Neşe Ömür Sibel Koparal Waseem Ahmad Khan

The main purpose of this paper is to define multiple alternative q-harmonic numbers, Hnk;q and multi-generalized q-hyperharmonic numbers of order r, Hnrk;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 Liq;k1,k2,…,kdt1,t2,…,td with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.