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)
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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 |
---|---|

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 |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Ana F. Loureiro |

Date Deposited: | 11 Oct 2012 15:21 UTC |

Last Modified: | 29 May 2019 09:33 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/31538 (The current URI for this page, for reference purposes) |

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