A parametrized generalization of Ohno's relation for multiple zeta values

TL;DR

This paper extends Ohno's relation to a parametrized family of multiple series, establishing new equivalences and deriving results for multiple zeta values.

Contribution

It introduces a parametrized generalization of Ohno's relation, connecting these series to multiple zeta values and their relations.

Findings

Parametrized multiple series satisfy Ohno's relation.

Established equivalence between relations of parametrized series and subfamilies.

Derived new results for multiple zeta values.

Abstract

In this paper, we prove that certain parametrized multiple series which generalize multiple zeta values satisfy the same relation as Ohno's relation for multiple zeta values. This is a parametrized generalization of Ohno's relation for multiple zeta values. By virtue of this generalization, we obtain a certain equivalence between the relation for the parametrized multiple series and its subfamily. As applications of the above results, we obtain some results for multiple zeta values.