Abstract
In this paper, we first give some results on monic generalized Hermite polynomials (GHP) {H-n((mu))(x)}(n >= 0), orthogonal with respect to the positive weight vertical bar x vertical bar(2 mu)e(-x2), mu > -1/2, x is an element of R, which will lead to the formulation of the second-order spectralvectorial differential equation (SVDE) that the GHP satisfies. This SVDE differs from the one given in G. Szego (problem 25. p. 380), which is a pseudo-spectral equation. Second, we give the SVDE, as conjecture, satisfied by the generalized Jacobi polynomials J(n)((alpha,alpha+1))(x, mu), orthogonal with respect to the positive weight w(x, alpha; mu) = vertical bar x vertical bar(-mu)(1 - x(2))(alpha)(1 - x), mu < 1, alpha > -1 on [-1,1].