A symbolic approach to multiple zeta values at the negative integers

TL;DR

This paper employs symbolic computation to derive explicit formulas, identities, and recurrences for the Euler-Zagier zeta function at negative integers, advancing understanding of multiple zeta values through analytic continuation.

Contribution

It introduces a symbolic approach to evaluate multiple zeta values at negative integers, providing new closed-form expressions and identities.

Findings

Explicit formulas for zeta values at negative integers

Contiguity identities and recurrences derived

Generation of new functional relations

Abstract

Symbolic computation techniques are used to derive some closed form expressions for an analytic continuation of the Euler-Zagier zeta function evaluated at the negative integers as recently proposed by B. Sadaoui. This approach allows to compute explicitly some contiguity identities, recurrences on the depth of the zeta values and generating functions.