Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function
type: Item
instance of: scholarly article
title: Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function
zbMATH Open document ID: 0945.41013
author: Ping Zhou
published in: Journal of Approximation Theory
publication date: 2000-08-28T00:00:00Z
review text: This paper is concerned with the explicit construction of the nonhomogeneous multivariate Padé approximants to a two variable version of a \(q\)-logarithm function \[ L_q(x,y)= \sum^\infty_{i,j =0}{(q-1) x^iy^i \over q^{i+j+1} -1}, \] for \(|q|>1\) and \(|x|, |y|<|q |\). The residue theorem and the functional equation method, introduced earlier by the author [J. Comput. Appl. Math. 79, No. 1, 1-17 (1997; Zbl 0865.41018); J. Approximation Theory 93, No. 2, 201-300 (1998; Zbl 0903.41007)], are used.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 33D70
zbMATH DE Number: 1423071
zbMATH Keywords: \(q\)-logarithm function
zbMATH Keywords: functional equation
zbMATH Keywords: multivariate Padé approximants
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
full work available at URL: jath.1999.3409
OpenAlex ID: W2068038588
cites work: Padé approximants for the q-elementary functions
cites work: Arithmetische Untersuchungen unendlicher Produkte
cites work: Padé approximants for operators: theory and applications
cites work: Multivariate Padé approximants revisited
cites work: A multivariate convergence theorem of the ``de Montessus de Ballore'' type
cites work: Q4040884
cites work: Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials
cites work: Q762656
cites work: Explicit construction of multivariate Padé approximants
cites work: Multivariate Padé approximants associated with functional relations
cites work: On the irrationality of the infinite product ∞Π j=0 (1+q −j r+q −2j s)
DOI: 10.1006/JATH.1999.3409
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description: scientific article; zbMATH DE number 1423071