Some relations of interpolated multiple zeta values

TL;DR

This paper establishes extended double shuffle relations for interpolated multiple zeta values, proves Hoffman's relations, and derives a generating function involving hypergeometric functions for sums of these values.

Contribution

It introduces new extended double shuffle relations and Hoffman's relations for interpolated multiple zeta values, along with a hypergeometric generating function representation.

Findings

Extended double shuffle relations established

Hoffman's relations proved for interpolated values

Generating function expressed via hypergeometric functions

Abstract

In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums of interpolated multiple zeta values of fixed weight, depth and height is represented by hypergeometric functions, and we discuss some special cases.