Some Symmetric Laguerre-Hahn linear Functionals of Class Six at Most

Zaatra Mohamed

Abstract


We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear
functional u dened by u = 􀀀x􀀀4v + 1
2
0
0 +0 is also regular and symmetric Laguerre-Hahn linear functional for
every complex except for a discrete set of numbers depending on v. We explicitly give the coecients of the
second-order recurrence relation of the orthogonal sequence associated with u and the class of the linear functional
u knowing that of v. Finally, we apply the above results to some examples.


Keywords


Orthogonal polynomials, Laguerre-Hahn linear functionals.

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