Linear differential equations and multiple zeta values. I. Zeta(2)
Volume 210 / 2010
Fundamenta Mathematicae 210 (2010), 207-242
MSC: Primary 05C38, 15A15; Secondary 05A15, 15A18.
DOI: 10.4064/fm210-3-1
Abstract
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 $\zeta (3).$
