Journal of Applied Mathematics
Volume 2004 (2004), Issue 2, Pages 137-167
doi:10.1155/S1110757X04402058
The second-order self-associated orthogonal sequences
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.
Abstract
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 s≤3. 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.