About semiclassical orthogonal polynomials of the class (2,2)

摘要

In the study of orthogonal polynomials (OP) associated to linear functionals u that verify a functional equation of the type D(A(z)u)=B(z)u, the polynomial B(z)−izA′(z) plays a very important role. In this paper we obtain the OP related to semiclassical functionals u belonging to the class (2,2) which are solutions of a functional equation as the above with A(z)=(z−α)2 and B(z)=b0z2+b1z+b2, where α is a root of B(z)−izA′(z)=0.