On a family of polynomials related to $\zeta (2,1)=\zeta (3)$

Abstract

We give a new proof of the identity $\zeta (\{2,1{\}}^l)=\zeta (\{3{\}}^l)$ of the multiple zeta values, where $l=1,2,\dots$, using generating functions of the underlying generalized polylogarithms. In the course of study we arrive at (hypergeometric) polynomials satisfying 3-term recurrence relations, whose properties we examine and compare with analogous ones of polynomials originated from an (ex-)conjectural identity of Borwein, Bradley and Broadhurst.

arXiv comment8 pages; v2: minor issues are addressed

References in corpus (1)

• Thirty-two Goldbach Variations