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Linear differential equations and multiple zeta-values. III. Zeta(3).
- Source :
-
Journal of Mathematical Physics . Jan2012, Vol. 53 Issue 1, p013507. 40p. 1 Diagram. - Publication Year :
- 2012
-
Abstract
- We consider the hypergeometric equation (1 - t)∂t∂t∂g + x3g = 0, whose unique analytic solution φ1(t; x) = 1 + O(t) near t = 0 for t = 1 becomes a generating function for multiple zeta values φ1(1; x) = f3(x) = 1 - ζ(3)x3 + ζ(3, 3)x6 - .... We apply the so-called WKB method to study solutions of the hypergeometric equation for large x and we calculate corresponding Stokes matrices. We prove that the function f3(x) near x = ∞ is also expressed via WKB type functions which subject to some Stokes phenomenon. This implies that f3(x) satisfies a sixth order linear differential equation with irregular singularity at infinity. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 53
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 70945554
- Full Text :
- https://doi.org/10.1063/1.3676076