On orthogonal polynomials with respect to the form \(-(x-c)S'\)
Let be \(S\) the classical Bessel or Jacobi linear functional and let \(u\) be the functional defined by \(u=-(x-c)S'\), which is, in general non regular. In this paper the authors establish necessary and sufficient conditions for the functional \(u\) to be regular. In fact, they proved in section 5 that under certain conditions (when \(u\) is regular), \(u\) is a semiclassical of class 1 and the corresponding orthogonal polynomial sequence satisfies certain algebraic relations (recurrence relations and structure relations) that characterize it. Finally, a concrete example of Jacobi type is worked out in details.
scientific article; zbMATH DE number 5082320