International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 70835, 19 pages

Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin

M. Sghaier1 and J. Alaya2

1Département de Mathématiques, Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Rue Omar Ibn El Khattab, 6072-Gabès, Tunisia
2Faculté des Sciences de Gabès, Université de Gabès, Route de Mednine, 6029-Gabès, Tunisia

Received 16 May 2005; Revised 4 March 2006; Accepted 4 May 2006

Copyright © 2006 M. Sghaier and J. Alaya. 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.


We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u=λx2v+δ0 is also regular and symmetric Laguerre-Hahn linear form for every complex λ except for a discrete set of numbers depending on v. We explicitly give the coefficients of the second-order recurrence relation, the structure relation of the orthogonal sequence associated with u, and the class of the linear form u knowing that of v. Finally, we apply the above results to the symmetric associated form of the first order for the classical polynomials.