On a system of ``classical'' polynomials of simultaneous orthogonality
type: Item
instance of: scholarly article
title: On a system of ``classical'' polynomials of simultaneous orthogonality
zbMATH Open document ID: 0857.42012
DOI: 10.1016/0377-0427(94)00129-4
published in: Journal of Computational and Applied Mathematics
publication date: 1997-03-12T00:00:00Z
review text: Let \(Q_{\overline n}(x)\), \(\overline n=(n_1,n_2)\), be the system of polynomials of simultaneous orthogonality [see \textit{E. M. Nikishin} and \textit{V. N. Sorokin}: ``Rational approximations and orthogonality'' (Russian orig. 1988; Zbl 0718.41002; Engl. transl. 1991; Zbl 0733.41001)] with \(\Delta_1=[a;0]\), \(\Delta_2=[0;1] (-1\leq a<0)\) and \(d\mu_i=|h(x)|dx\), \(h(x)=(x-a)^\alpha(x-1)^\beta x^\gamma\) \((\alpha,\beta,\gamma>-1)\). The differential equation of third-order, the limit periodic behaviour of recurrence coefficients, and the ratio asymptotics for those polynomials are obtained.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 908369
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Padé approximations
author: V. A. Kaliaguine
author: A. Ronveaux
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00129-4
OpenAlex ID: W2037499164
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description: scientific article; zbMATH DE number 908369