Loureiro, Ana F.
(2010)
*
New results on the Bochner condition about classical orthogonal polynomials.
*
Journal of Mathematical Analysis and Applications,
364
(2).
pp. 307-323.
ISSN 0022-247X.
(doi:10.1016/j.jmaa.2009.12.003)
(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:31561)

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.2009.12.003 |

## Abstract

The classical polynomials (Hermite, Laguerre, Bessel and Jacobi) are the only orthogonal polynomial sequences (OPS) whose elements are eigenfunctions of the Bochner second-order differential operator F (Bochner, 1929 [3]). In Loureiro, Maroni and da Rocha (2006) [18] these polynomials were described as eigenfunctions of an even order differential operator Fk with polynomial coefficients defined by a recursive relation. Here, an explicit expression of Fk for any positive integer k is given. The main aim of this work is to explicitly establish sums relating any power of F with Fk, k?1, in other words, to bring a pair of inverse relations between these two operators. This goal is accomplished with the introduction of a new sequence of numbers: the so-called A-modified Stirling numbers, which could be also called as Bessel or Jacobi–Stirling numbers, depending on the context and the values of the complex parameter A.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1016/j.jmaa.2009.12.003 |

Uncontrolled keywords: | Classical orthogonal polynomials; Bochner differential equation; Stirling numbers; Bessel–Stirling numbers; Jacobi–Stirling numbers; Inverse relations |

Subjects: | Q Science > QA Mathematics (inc Computing science) > QA351 Special functions |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Ana F. Loureiro |

Date Deposited: | 11 Oct 2012 15:17 UTC |

Last Modified: | 16 Nov 2021 10:09 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/31561 (The current URI for this page, for reference purposes) |

Loureiro, Ana F.: | https://orcid.org/0000-0002-4137-8822 |

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