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We show that if v is a symmetric regular Laguerre-Hahn linearform (functional), then the linear form u defined by u=−λx−2v+δ0 is also regular and symmetric Laguerre-Hahnlinear form for every complex λ except for a discrete setof numbers depending on v. We explicitly give the coefficientsof the second-order recurrence relation, the structure relation ofthe orthogonal sequence associated with u, and the class of thelinear form u knowing that of v. Finally, we apply the aboveresults to the symmetric associated form of the first order forthe classical polynomials

international journal of mathematics and mathematical sciences

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