The search for differential equations for certain sets of orthogonal polynomials

Abstract

We look for differential equations of the form Σ ∞ i=0 c i ( x) y ( i) ( x) = 0, where the coefficients { c i ( x)} ∞ i=0 are continuous functions on the real line and where { c i ( x)} ∞ i=1 are independent of n, for the generalized Jacobi polynomials { P α, β, M, N n ( x)} ∞ n=0 and for generalized Laguerre polynomials { L α, M, N n ( x)} ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We use a method involving computer algebra packages like Maple and Mathematica and we will give some preliminary results.