Abstract
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.
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