Interpolation of q-analogue of multiple zeta and zeta-star values

We know at least two ways to generalize multiple zeta(-star) values, or MZ(S)Vs for short, which are q-analogue and t-interpolation. The q-analogue of MZ(S)Vs, or qMZ(S)Vs for short, was introduced by Bradley, Okuda and Takeyama; Zhao, etc. On the other hand, the polynomials interpolating MZVs and MZSVs using a parameter t were introduced by Yamamoto. We call these t-MZVs. In this paper, we consider such two generalizations simultaneously, that is, we compose polynomials, called t-qMZVs, interpolating qMZVs and qMZSVs using a parameter t which are reduced to qMZVs as t = 0, to qMZSVs as t = 1, and to t-MZVs as q -> 1. Then we prove Kawashima type relation, cyclic sum formula and Hoffman type relation for t-qMZVs. (C) 2016 Elsevier Inc. All rights reserved.