Contiguous relations, continued fractions and orthogonality: An \(_ 8\varphi_ 7\) model
type: Item
instance of: scholarly article
title: Contiguous relations, continued fractions and orthogonality: An \(_ 8\varphi_ 7\) model
zbMATH Open document ID: 0853.33014
DOI: 10.1016/0377-0427(95)00115-8
author: David R. Masson
author: Dharma P. Gupta
published in: Journal of Computational and Applied Mathematics
publication date: 1995-01-01T00:00:00Z
review text: In this extremely interesting paper the authors start with a contiguous relation for the very well posed \(_8 \varphi_7\) basic hypergeometric function \[ W : =_8 \varphi_7 \left( \begin{matrix} a,\;q \sqrt a,\;- q \sqrt a,\;b, \;c,\;d,\;e, \;f \\ \sqrt a,\;- \sqrt a,\;{aq \over b}, {aq \over c}, \dots, {aq \over f} \end{matrix} ;{a^2q^2 \over bcdef} \right). \] From this they obtain a three-term recurrence relation and thus a continued fraction expansion for the ratio of two ``consecutive \(Ws\)''. By solving the recurrence relation completely, they find the value of the continued fraction. For special values of the parameters the continued fraction terminates. For this situation the authors prove that there is an associated system of biorthogonal rational functions. This finite, discrete biorthogonality is explicitly given in the paper.
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 903570
zbMATH Keywords: discrete biorthogonality
reviewed by: Lisa Lorentzen
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00115-8
OpenAlex ID: W2056579616
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
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description: scientific article; zbMATH DE number 903570