Around q-Appell polynomial sequences

Loureiro, Ana F. and Maroni, P. (2011) Around q-Appell polynomial sequences. Ramanujan Journal, 26 (3). pp. 311-321. ISSN 1382-4090. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1007/s11139-011-9336-8

Abstract

First we show that the quadratic decomposition of the Appell polynomials with respect to the q-divided difference operator is supplied by two other Appell sequences with respect to a new operator Mq;q-eq;q−, where ε represents a complex parameter different from any negative even integer number. While seeking all the orthogonal polynomial sequences invariant under the action of MÖq;q-e/2q;q−2 (the MÖq;q-e/2q;q−2 -Appell), only the Wall q-polynomials with parameter q ε/2+1 are achieved, up to a linear transformation. This brings a new characterization of these polynomial sequences.

Item Type: Article
Uncontrolled keywords: Orthogonal polynomials; Appell sequences; Lowering operators; q-derivative; Hahn’s operator; Quadratic decomposition
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Ana F. Loureiro
Date Deposited: 11 Oct 2012 14:54
Last Modified: 12 Feb 2013 16:18
Resource URI: https://kar.kent.ac.uk/id/eprint/31547 (The current URI for this page, for reference purposes)
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