On the duality formula for parametrized multiple series

TL;DR

This paper explores a duality formula for parametrized multiple series, deriving new relations among multiple zeta and Hurwitz zeta values, extending known identities like Ohno's relation.

Contribution

It introduces a novel duality formula that generates new identities among extended multiple zeta and Hurwitz zeta values, expanding the theoretical framework.

Findings

New duality formula for parametrized multiple series

Derived a new relation among extended multiple zeta values

Established a new identity for multiple Hurwitz zeta values

Abstract

We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple zeta values. We do the same study also to multiple Hurwitz zeta values, and obtain a new identity for them.