Some results on q-multiple harmonic sums

Abstract

In this paper the author present some new identities for $q$-analogues of multiple harmonic (star) sums whose indices are the sequences $(\{p\}_a)$ and $(\{p\}_a,p+1,\{p\}_b)$. Then we use these formulas to establish some relations between multiple harmonic (star) sums and classical harmonic numbers and binomial coefficients. As a application we give some explicit formulas involving multiple zeta star values. Some interesting consequences and illustrative examples are also given.