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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A Laguerre polynomial sequence of parameter ε/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) ] 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.
|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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