Loureiro, Ana F., Maroni, P., 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. (doi:10.1016/j.jmaa.2005.09.026) (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) (KAR id:31538)
| 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. | |
| Official URL: http://dx.doi.org/10.1016/j.jmaa.2005.09.026 |
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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 |
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| DOI/Identification number: | 10.1016/j.jmaa.2005.09.026 |
| Uncontrolled keywords: | Classical orthogonal polynomials; Classical forms; Bochner's differential equation |
| Subjects: | Q Science > QA Mathematics (inc Computing science) > QA351 Special functions |
| Institutional Unit: | Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences |
| Former Institutional Unit: |
Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
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| Depositing User: | Ana F. Loureiro |
| Date Deposited: | 11 Oct 2012 15:21 UTC |
| Last Modified: | 20 May 2025 11:35 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/31538 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Loureiro, Ana F..
| Creator's ORCID: |
 https://orcid.org/0000-0002-4137-8822
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