Extensions of some results of P. Humbert on Bezoutʹs identity for classical orthogonal polynomials

In this paper, the Bezoutʹs identity is analyzed in the context of classical orthogonal polynomials solution of a second order differential equation of hypergeometric type. Differential equations, relation with the starting family as well as recurrence relations and explicit representations are given for the Bezoutʹs pair. Extensions to classical orthogonal polynomials of a discrete variable and their q-analogues are also presented. Applications of these results for the representation of the second kind functions are given.