Maesaka-Seki-Watanabe's formula for multiple harmonic $q$-sums

Abstract

Maesaka, Seki, and Watanabe recently discovered an equality called the MSW formula. This paper provides a $q$-analogue of the MSW formula. It discusses the new proof of the duality relation for finite multiple harmonic $q$-series at primitive roots of unity via $q$-analogue of the MSW formula. This paper also gives a $q$-analogue of Yamamoto's generalization of the MSW formula for Schur type.

12 pages