On three general forms of multiple zeta(-star) values

TL;DR

This paper explores three broad types of multiple zeta(-star) values, deriving new sum formulas for specific cases and providing a novel proof for an existing sum formula, advancing understanding in this mathematical area.

Contribution

It introduces three general forms of multiple zeta(-star) values and derives new sum formulas and an alternative proof for a known sum formula.

Findings

New sum formulas for multiple zeta values with height ≤ 2

Evaluation of zeta^\u2217(1^m,2^{n+1})

A new proof of the sum formula for multiple zeta values

Abstract

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of $\zeta^\star(\{1\}^m,\{2\}^{n+1})$. We also give a new proof of sum formula of multiple zeta values.