Quadratic decomposition of Laguerre polynomials via lowering operators

Loureiro, Ana F. and Maroni, P. (2011) Quadratic decomposition of Laguerre polynomials via lowering operators. Journal of Approximation Theory, 163 (7). pp. 888-903. ISSN 0021-9045. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1016/j.jat.2010.07.009

Abstract

A Laguerre polynomial sequence of parameter ε/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) [28]] as an orthogonal Fε-Appell sequence, where Fε represents a lowering (or annihilating) operator depending on the complex parameter ε≠−2n for any integer n⩾0. Here, we proceed to the quadratic decomposition of an Fε-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 Gε,μ, where μ is either 1 or −1. Therefore, we introduce and develop the concept of the Gε,μ-Appell sequences and we prove that they cannot be orthogonal. Finally, the quadratic decomposition of the non-symmetric sequence of Laguerre polynomials (with parameter ε/2) is fully accomplished.

Item Type: Article
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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Ana F. Loureiro
Date Deposited: 11 Oct 2012 15:08
Last Modified: 19 Feb 2013 12:24
Resource URI: http://kar.kent.ac.uk/id/eprint/31555 (The current URI for this page, for reference purposes)
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