Quadratic decomposition of Appell sequences

Loureiro, Ana F. and Maroni, P. (2008) Quadratic decomposition of Appell sequences. Expositiones Mathematicae, 26 (2). pp. 177-186. ISSN 0723-0869. (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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We proceed to the quadratic decomposition of Appell sequences and we characterise the four derived sequences obtained by this approach. We prove that the two monic polynomial sequences associated to such quadratic decomposition are also Appell sequences with respect to another (lowering) operator, which we call as Fɛ, where either ɛ=1 or -1. Thus, we introduce and develop the concept of the Appell polynomial sequences with respect to the operator Fɛ (where, ɛ is a parameter belonging to the field of the complex numbers): the Fɛ-Appell sequences. The orthogonal polynomial sequences that are also Fɛ-Appell correspond to the Laguerre sequences with parameter ɛ/2. Indeed, this brings an entirely new characterisation of the Laguerre sequences.

Item Type: Article
Uncontrolled keywords: Orthogonal polynomials; Appell sequences; Classical polynomials; Quadratic decomposition; Hermite polynomials; Laguerre polynomials; Lowering operator
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 15:20
Last Modified: 20 Feb 2013 14:43
Resource URI: https://kar.kent.ac.uk/id/eprint/31563 (The current URI for this page, for reference purposes)
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