Hermite-Padé polynomials associated with certain generalized hypergeometric functions
type: Item
instance of: scholarly article
title: Hermite-Padé polynomials associated with certain generalized hypergeometric functions
zbMATH Open document ID: 0688.41021
DOI: 10.1016/0021-9045(89)90039-7
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: Continuing his previous study [ibid. 42, 299-386 (1984; Zbl 0565.41015)], the author constructs two types of Hermite-Padé polynomials associated with the functions \(1,_ pF_{p-1}\left( \begin{matrix} a\\ c\end{matrix} ;x\right)\) and p-1 additional functions contiguous with this generalized hypergeometric function. The author uses some properties of Riemann modules and other techniques due to G. V. Chudnovsky and introduced the so-called augmented modules. The results of the paper under review might lead to the determination of the asymptotic behaviour of the Hermite- Padé polynomials and to shed some light on the author's earlier conjectures on this subject.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4127814
zbMATH Keywords: Hermite-Padé polynomials
zbMATH Keywords: generalized hypergeometric function
zbMATH Keywords: Riemann modules
zbMATH Keywords: augmented modules
author: John Nuttall
reviewed by: Ion Badea
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90039-7
OpenAlex ID: W2033200936
cites work: Padé approximations to the generalized hypergeometric functions. I
cites work: Q3878107
cites work: Multi-dimensional generalizations of the Padé table
cites work: Asymptotics of diagonal Hermite-Padé polynomials
cites work: Relations among the fundamental solutions of the generalized hypergeometric equation when 𝑝=𝑞+1. I. non-logarithmic cases
description: scientific article; zbMATH DE number 4127814