Note on cyclic sum of certain parametrized multiple series

TL;DR

This paper proves new cyclic sum formulas for two-parameter multiple series, extending known results for multiple zeta values and their star variants, thereby broadening the understanding of these mathematical objects.

Contribution

It introduces novel cyclic sum formulas for parametrized multiple series, generalizing existing results for multiple zeta and zeta-star values.

Findings

Established cyclic sum formulas for two-parameter multiple series.

Generalized known formulas for multiple zeta values.

Provided non-trivial extensions to existing mathematical theory.

Abstract

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.