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Quadratic decomposition of Laguerre polynomials via lowering operators

Loureiro, Ana F., Maroni, P. (2011) Quadratic decomposition of Laguerre polynomials via lowering operators. Journal of Approximation Theory, 163 (7). pp. 888-903. ISSN 0021-9045. (doi:10.1016/j.jat.2010.07.009) (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)

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. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.jat.2010.07.009

Abstract

A Laguerre polynomial sequence of parameter ?/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) [28]] as an orthogonal F?-Appell sequence, where F? represents a lowering (or annihilating) operator depending on the complex parameter ???2n for any integer n?0. Here, we proceed to the quadratic decomposition of an F?-Appell sequence, and we conclude that the four sequences obtained by this approach are also Appell but with respect to another lowering operator consisting of a Fourth-order linear differential operator G?,?, where ? is either 1 or ?1. Therefore, we introduce and develop the concept of the G?,?-Appell sequences and we prove that they cannot be orthogonal. Finally, the quadratic decomposition of the non-symmetric sequence of Laguerre polynomials (with parameter ?/2) is fully accomplished.

Item Type: Article
DOI/Identification number: 10.1016/j.jat.2010.07.009
Uncontrolled keywords: Orthogonal polynomials; Laguerre polynomials; Appell polynomials; Lowering operator; Genocchi numbers
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Ana F. Loureiro
Date Deposited: 11 Oct 2012 15:08 UTC
Last Modified: 29 May 2019 09:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31555 (The current URI for this page, for reference purposes)
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