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.
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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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