Analytic properties of Ohno function

TL;DR

This paper investigates the Ohno function, a complex interpolation of Ohno's relation on multiple zeta values, exploring its properties, new expressions, relations, and providing a direct proof of the relation's interpolation.

Contribution

It introduces new expressions and relations for the Ohno function and offers a direct proof of its interpolation of Ohno's relation.

Findings

Identified the region of absolute convergence for the Ohno function

Derived new expressions and relations of the Ohno function

Provided a direct proof of the interpolation of Ohno's relation

Abstract

Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.