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

• Autorzy: Michał Zakrzewski , Henryk Żołądek
• Języki publikacji: EN

Abstrakty

EN

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 ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).

Kategorie tematyczne

• 15A15: Determinants, permanents, other special matrix functions
• 05A15: Exact enumeration problems, generating functions
• 05C38: Paths and cycles
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 3
• Strony: 207-242

Daty

wydano

2010

Twórcy

autor

Michał Zakrzewski

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

autor

Henryk Żołądek

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

Identyfikatory

DOI

10.4064/fm210-3-1