Orthogonal Polynomials Associated with Some Modification
of a Linear Form

Sghaier, M.; Alaya, J.

Orthogonal Polynomials Associated with Some Modification of a Linear Form

Sghaier, M. ; Alaya, J.

Methods Appl. Anal., Tome 11 (2004) no. 1, p. 267-294 / Harvested from Project Euclid

Résumé

We show that if v is a regular Laguerre-Hahn (resp. semiclassical) linear form,then the linear form u defined by the relation LAMBDA(x - a )u = (x - c)v is also regular and a Laguerre-Hahn (resp. semiclassical) linear form for every complex LAMBDA except for a discrete set of numbers depending on v, a, and c. We give explicitly the coefficients of the three-term 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 some examples.

Publié le : 2004-06-14
Classification:

@article{1119019657,
     author = {Sghaier, M. and Alaya, J.},
     title = {Orthogonal Polynomials Associated with Some Modification
of a Linear Form},
     journal = {Methods Appl. Anal.},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 267-294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1119019657}
}

Sghaier, M.; Alaya, J. Orthogonal Polynomials Associated with Some Modification
of a Linear Form. Methods Appl. Anal., Tome 11 (2004) no. 1, pp.  267-294. http://gdmltest.u-ga.fr/item/1119019657/