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

We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u = − λ x − 2 v + δ 0 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.