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