Ohno-type relation for interpolated multiple zeta values

TL;DR

This paper establishes Ohno-type relations for interpolated multiple zeta values and finite variants, providing new sum formulas and extending previous results by Yamamoto and Seki.

Contribution

It introduces the Ohno-type relation for interpolated multiple zeta values and their finite counterparts, expanding the theoretical framework of multiple zeta value relations.

Findings

Proved Ohno-type relations for interpolated multiple zeta values

Derived sum formulas for interpolated and $ ext{F}$-multiple zeta values

Extended relations to finite multiple zeta values

Abstract

We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for interpolated multiple zeta values and interpolated $\mathcal{F}$-multiple zeta values, which were proved by Yamamoto and Seki, respectively.