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

Pitu Sarkar, Nita Tamang

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.

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

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.

Paper Structure

This paper contains 4 sections, 11 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem $1$
  3. Recursive formula for t-stuffle product
  4. Some Applications

Key Result

Theorem 1

For integers $m,u \geq 2, p \geq 1 \text{ and } n,v \geq 0$,

Theorems & Definitions (18)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Corollary 1
  • Proposition 1
  • proof
  • Corollary 2
  • proof
  • Lemma 1
  • proof
  • ...and 8 more