An interpolation of Bradley's sum formula

TL;DR

This paper generalizes Bradley's sum formula for $q$-multiple zeta values to the broader context of the $q$-multiple zeta function, expanding the theoretical framework of these special functions.

Contribution

It introduces a new generalized sum formula for the $q$-multiple zeta function, extending existing relations for $q$-multiple zeta values.

Findings

Established a generalized sum formula for the $q$-multiple zeta function.

Extended the theoretical understanding of $q$-multiple zeta relations.

Abstract

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.