Loureiro, Ana F. and Maroni, P.
(2008)
*Quadratic decomposition of Appell sequences.*
Expositiones Mathematicae, 26
(2).
pp. 177-186.
ISSN 0723-0869.
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Official URL http://dx.doi.org/10.1016/j.exmath.2007.10.002 |

## Abstract

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: | http://kar.kent.ac.uk/id/eprint/31563 (The current URI for this page, for reference purposes) |

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