The generalized Bochner condition about classical orthogonal polynomials revisited

• Type: Article in International Scientific Journal
• Date: 2006

Authors

Loureiro, AF (Author) Other; Maroni, P (Author) Other; da Rocha, Z (Author) FCUP

Journal

Title: Journal of Mathematical Analysis and Applications

Vol. 322

Pages: 645-667

ISSN: 0022-247X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-GKG

DOI: 10.1016/j.jmaa.2005.09.026

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23