On a t-stuffle product formula for interpolated multiple zeta values

TL;DR

This paper develops a restricted decomposition formula and recursive method for the t-stuffle product of interpolated multiple zeta values, using combinatorial techniques and induction, advancing the algebraic understanding of these special functions.

Contribution

It introduces a new restricted decomposition formula and recursive approach for the t-stuffle product in interpolated multiple zeta values, with combinatorial and inductive proofs.

Findings

Derived a restricted decomposition formula for interpolated multiple zeta values.

Established a recursive formula for the t-stuffle product.

Provided combinatorial and inductive proofs for key results.

Abstract

In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both cases, combinatorial description of t-stuffle product is our basic tool. We also provide alternative proofs by mathematical induction for some of the results.