Another proof of Zagier's evaluation formula of the multiple zeta values $\zeta(2,...,2,3,2,...,2)$

TL;DR

This paper provides an alternative proof of Zagier's evaluation formula for specific multiple zeta values using transformation formulas of hypergeometric series.

Contribution

It introduces a new proof method for Zagier's formula leveraging hypergeometric series transformations, offering deeper insight into multiple zeta value evaluations.

Findings

Validates Zagier's evaluation formula through hypergeometric transformations

Offers a new proof technique for multiple zeta value formulas

Enhances understanding of hypergeometric series in number theory

Abstract

Using some transformation formulas of the generalized hypergeometric series $\,_3F_2$, we give another proof of D. Zagier's evaluation formula of the multiple zeta values $\zeta(2,...,2,3,2,...,2)$.