Double tails of multiple zeta values

TL;DR

This paper introduces double tails of multiple zeta values, explores their recurrence relations, generalizes Euler's formula to all multiple zeta values, and presents an efficient computation algorithm.

Contribution

It presents the concept of double tails for multiple zeta values, establishes their recurrence relations, and offers a new algorithm for their computation.

Findings

Recurrence relations for double tails of multiple zeta values

Generalization of Euler's formula to all multiple zeta values

Development of an efficient computational algorithm

Abstract

In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula $\zeta(2)=3\sum_{m=1}^\infty m^{-2}\left({2m\atop m}\right)^{-1}$ to all multiple zeta values, as well as a new and very efficient algorithm for computing these values.