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Some Basic 𝑑-Orthogonal Polynomial Sets

Some Basic 𝑑-Orthogonal Polynomial Sets The purpose of this paper is to study the class of polynomial sets which are at the same time 𝑑-orthogonal and 𝑞-Appell. By a linear change of variable, the resulting set reduces to 𝑞-Al-Salam–Carlitz polynomials, for 𝑑 = 1. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order 𝑑 + 1. We also explicitly express a 𝑑-dimensional functional for which the d-orthogonality holds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Some Basic 𝑑-Orthogonal Polynomial Sets

Georgian Mathematical Journal , Volume 12 (4) – Dec 1, 2005

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References (27)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2005.583
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to study the class of polynomial sets which are at the same time 𝑑-orthogonal and 𝑞-Appell. By a linear change of variable, the resulting set reduces to 𝑞-Al-Salam–Carlitz polynomials, for 𝑑 = 1. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order 𝑑 + 1. We also explicitly express a 𝑑-dimensional functional for which the d-orthogonality holds.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2005

Keywords: Orthogonal polynomials; 𝑑-orthogonal polynomials; 𝑑-dimensional functional; 𝑞-difference operator

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