Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 137-167

The second-order self-associated orthogonal sequences

P. Maroni1 and M. Ihsen Tounsi2

1Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie—Centre National de la Recherche Scientifique (CNRS), Boîte courrier 187, Paris Cedex 05 75252, France
2Institut Supérieur des Sciences Appliquées et de Téchnologies Gabès, Route de Medenine, Gabès, Tunisia

Received 13 February 2004

Copyright © 2004 P. Maroni and M. Ihsen Tounsi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this work is to describe the orthogonal polynomials sequences which are identical to their second associated sequence. The resulting polynomials are semiclassical of class s3. The characteristic elements of the structure relation and of the second-order differential equation are given explicitly. Integral representations of the corresponding forms are also given. A striking particular case is the case of the so-called electrospheric polynomials.