Classical Orthogonal Polynomials Revisited

Abstract This manuscript contains a small portion of the algebraic theory orthogonal polynomials developed by Maroni and their applicability to study characterization classical families, namely Hermite, Laguerre, Jacobi, Bessel polynomials. It is presented cyclical proof some most relevant characterizations, particularly those due Al-Salam Chihara, Bochner, Hahn, Maroni, McCarthy. Two apparently new characterizations are also added. Moreover, it proved through an equivalence relation that, up constant factors affine changes variables, four families named above only