Linear differential equations and multiple zeta values. I. Zeta(2)

Micha/l Zakrzewski ¹   ; Henryk /Zo/l/adek ¹

¹ Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland

Fundamenta Mathematicae, Tome 210 (2010) no. 3, pp. 207-242

Résumé

Certain generating fuctions for multiple zeta values are expressed as values at some point of solutions of linear meromorphic differential equations. We apply asymptotic expansion methods (like the WKB method and the Stokes operators) to solutions of these equations. In this way we give a new proof of the Euler formula $\zeta (2)=\pi ^{2}/6.$ In further papers we plan to apply this method to study some third order hypergeometric equation related to $\zeta (3).$

Détail

DOI : 10.4064/fm210-3-1

Keywords: certain generating fuctions multiple zeta values expressed values point solutions linear meromorphic differential equations apply asymptotic expansion methods wkb method stokes operators solutions these equations proof euler formula zeta further papers plan apply method study third order hypergeometric equation related zeta