Multipoint Hermite-Padé approximations for beta functions
type: Item
instance of: scholarly article
title: Multipoint Hermite-Padé approximations for beta functions
zbMATH Open document ID: 1202.41008
DOI: 10.1134/S000143461001027X
author: A. A. Kandayan
author: V. N. Sorokin
published in: Mathematical Notes
publication date: 2010-09-24T00:00:00Z
review text: The authors construct the multipoint Hermite-Padé approximant \(P_n/Q_n\) to the function \(f_\alpha(z)=B(\alpha,z)\) meromorphic on the entire complex plane and having simple poles at the points \(-m\) (\(m\in\mathbb{Z}\)), where \(B(p,q)=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}\) is the beta function. \(P_n/Q_n\) is defined as follows: \(R_n(z)=Q_n(z)f_\alpha(z)-P_n(z)\) and satisfy the interpolation condition \(R_n(\beta +k)=0\) for some \(\beta>0\) and \(k=0, \ldots,2n\). They prove that the uniform limite distribution of the zeros of the polynomials \(Q_n\) exists.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 5791039
zbMATH Keywords: Hermite-Padé approximations
zbMATH Keywords: beta function
zbMATH Keywords: Nikishin system
zbMATH Keywords: logarithmic potential
zbMATH Keywords: asyptotic behavior
zbMATH Keywords: Mittag-Leffer expansion
zbMATH Keywords: Rodrigues formula
MaRDI profile type: Publication
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cites work: Q3904824
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full work available at URL: s000143461001027x
OpenAlex ID: W2007634817
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description: scientific article; zbMATH DE number 5791039