The Search for Differential Equations for Certain Sets of Orthogonal Polynomials
نویسنده
چکیده
We look for differential equations of the form ∞ ∑ i=0 ci(x)y (x) = 0, where the coefficients {ci(x)} ∞ i=0 are continuous functions on the real line and where {ci(x)} ∞ i=1 are independent of n, for the generalized Jacobi polynomials { P n (x) } ∞ n=0 and for generalized Laguerre polynomials { L n (x) } ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We use a method involving computeralgebra packages like Maple and Mathematica and we will give some preliminary results. AMS Subject Classification : 33A65, 33C45, 34A35
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