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June 2004 Orthogonal Polynomials Associated with Some Modification of a Linear Form
J. Alaya, M. Sghaier
Methods Appl. Anal. 11(2): 267-294 (June 2004).


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.


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J. Alaya. M. Sghaier. "Orthogonal Polynomials Associated with Some Modification of a Linear Form." Methods Appl. Anal. 11 (2) 267 - 294, June 2004.


Published: June 2004
First available in Project Euclid: 17 June 2005

zbMATH: 1078.42018
MathSciNet: MR2143523

Rights: Copyright © 2004 International Press of Boston


Vol.11 • No. 2 • June 2004
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