LADDER OPERATORS AND DIFFERENTIAL-EQUATIONS FOR ORTHOGONAL POLYNOMIALS

Under some integrability conditions we derive raising and lowering dif ferential recurrence relations for polynomials orthogonal with respect to a weight function supported in the real line. We also derive a sec ond-order differential equation satisfied by these polynomials. We dis cuss the Lie algebra generated by the generalized creation and annihil ation operators. From the differential equations, Plancherel-Rotach ty pe asymptotics are derived. Under certain conditions, stated in the te xt, an Airy function emerges.