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

Michał Zakrzewski, and Henryk Żołądek. "Linear differential equations and multiple zeta values. I. Zeta(2)." Fundamenta Mathematicae 210.3 (2010): 207-242. <http://eudml.org/doc/282621>.

@article{MichałZakrzewski2010,
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 ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).},
author = {Michał Zakrzewski, Henryk Żołądek},
journal = {Fundamenta Mathematicae},
keywords = {generating functions for multiple zeta values; solutions of linear meromorphic differential equations; asymptotic expansion methods; WKB method; Stokes operators; Euler formula for },
language = {eng},
number = {3},
pages = {207-242},
title = {Linear differential equations and multiple zeta values. I. Zeta(2)},
url = {http://eudml.org/doc/282621},
volume = {210},
year = {2010},
}

TY - JOUR
AU - Michał Zakrzewski
AU - Henryk Żołądek
TI - Linear differential equations and multiple zeta values. I. Zeta(2)
JO - Fundamenta Mathematicae
PY - 2010
VL - 210
IS - 3
SP - 207
EP - 242
AB - 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).
LA - eng
KW - generating functions for multiple zeta values; solutions of linear meromorphic differential equations; asymptotic expansion methods; WKB method; Stokes operators; Euler formula for
UR - http://eudml.org/doc/282621
ER -