The complementary polynomials and the Rodrigues operator . A distributional study

We can write the polynomial solution of the second order linear differential equation of hypergeometric-type φ(x)y + ψ(x)y + λy = 0, where φ and ψ are polynomials, deg φ ≤ 2, degψ = 1 and λ is a constant, among others, by using the Rodrigues operator Rk(φ,u) (see [3]) where u is certain linear operator which satisfies the distributional equation