International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 7, Pages 70835, 19 p.
doi:10.1155/IJMMS/2006/70835
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
Abstract
We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u=−λx−2v+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.