The generalised Bochner condition about classical orthogonal polynomials revisited

Loureiro, Ana F. and Maroni, P. and Rocha, Z. da (2006) The generalised Bochner condition about classical orthogonal polynomials revisited. Journal of Mathematical Analysis and Applications, 322 (2). pp. 645-667. ISSN 0022-247X. (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.jmaa.2005.09.026

Abstract

We bring a new proof for showing that an orthogonal polynomial sequence is classical if and only if any of its polynomial fulfils a certain differential equation of order 2k, for some k⩾1. So, we build those differential equations explicitly. If k=1, we get the Bochner's characterization of classical polynomials. With help of the formal computations made in Mathematica, we explicitly give those differential equations for k=1,2 and 3 for each family of the classical polynomials. Higher order differential equations can be obtained similarly.

Item Type: Article
Uncontrolled keywords: Classical orthogonal polynomials; Classical forms; Bochner's differential equation
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 15:21
Last Modified: 20 Feb 2013 14:41
Resource URI: http://kar.kent.ac.uk/id/eprint/31538 (The current URI for this page, for reference purposes)
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