Multiple series expressions for the Newton series which interpolate finite multiple harmonic sums

TL;DR

This paper demonstrates that Newton series interpolating finite multiple harmonic sums can be expressed as multiple series, providing new formulas for multiple zeta values that include duality relations.

Contribution

It introduces a novel representation of Newton series as multiple series, advancing the understanding of their structure and applications to multiple zeta values.

Findings

Newton series can be written as multiple series

New formulas for multiple zeta values including duality

Enhanced understanding of harmonic sums and MZV relations

Abstract

The Newton series which interpolate finite multiple harmonic sums are useful in the study of multiple zeta values (MZV's). In this paper, we prove that these Newton series can be written as multiple series. As an application, we give a formula for MZV's which contains the duality.