ON THE SUM FORMULA FOR MULTIPLE q-ZETA VALUES

Abstract. Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q → 1. Here, we discuss the sum formula for multiple q-zeta values, and provide a self-contained proof. As a consequence, we also derive a q-analog of Euler’s evaluation of the double zeta function ζ(m, 1).