Title: Apéry Polynomials and the multivariate Saddle Point Method
Authors: Neuschel, Thorsten # ×
Issue Date: Dec-2014
Publisher: Springer-Verlag New York
Series Title: Constructive Approximation vol:40 issue:3 pages:487-507
Abstract: The Apéry polynomials and in particular their asymptotic behavior play an essential role in the understanding of the irrationality of ζ(3). In this paper, we present a method to study the asymptotic behavior of the sequence of Apéry polynomials in the whole complex plane as n tends to infinity. The proofs are based on a multivariate version of the complex saddle point method. Moreover, the asymptotic zero distributions for the polynomials and for some transformed Apéry polynomials are derived by means of the theory of logarithmic potentials with external fields, establishing a characterization as the unique solution of a weighted equilibrium problem. The method applied is a general one, so that the treatment can serve as a model for the study of objects related to the Apéry polynomials.
ISSN: 0176-4276
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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