Uniform convergence of rows of the Padé table for functions with smooth Maclaurin series coefficients
type: Item
instance of: scholarly article
title: Uniform convergence of rows of the Padé table for functions with smooth Maclaurin series coefficients
zbMATH Open document ID: 0621.41010
DOI: 10.1007/BF01890573
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: Given a formal power series \(f(z):=\sum^{\infty}_{j=0}a_ jz^ j\) for which the quantity \(a_{j-1}a_{j+1}/a^ 2_ j\) has a prescribed asymptotic behavior as \(j\to \infty\), we obtain the asymptotic behavior of poles of rows of the Padé table, and the associated Toeplitz determinants. In particular, we can show for large classes of entire functions of zero, finite, and infinite order (including the Mittag- Leffler functions) and for \(N=1,2,3,...\), that the poles of [m/n](z) approach \(\infty\) with rate \(a_ m/a_{m+1}\) as \(m\to \infty\).
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 4006895
zbMATH Keywords: Padé approximators
zbMATH Keywords: power series coefficients
zbMATH Keywords: Padé table
zbMATH Keywords: Toeplitz determinants
zbMATH Keywords: Mittag-Leffler functions
author: Doron S. Lubinsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4006895