Generalized Euler decomposition formula for interpolated multiple zeta values

TL;DR

This paper introduces a generalized Euler decomposition formula for interpolated multiple zeta values using a new t-shuffle product, with proofs via combinatorial and recursive methods, expanding understanding of these special functions.

Contribution

It presents a novel generalized Euler decomposition formula for interpolated multiple zeta values and offers two different proofs for the height one case.

Findings

Derived a general t-shuffle product formula

Established a generalized Euler decomposition formula

Provided combinatorial and recursive proofs for height one case

Abstract

In this paper, we obtain a general t-shuffle product formula, using which we derive a generalized Euler decomposition formula for interpolated multiple zeta values. We also provide the same formula in case of height one through two different approaches: one by combinatorial description and another one by recursive formula.