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. (Contact us about this Publication) | |
| 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) |
- Depositors only (login required):
