Search for Differential Equations for Orthogonal Polynomials by Using Computers

摘要

Differential equations are examined of the form Summation, i = 0 to i = infinity,of (c(sub i)(x)y(sup i)(x)) = lambda(sub n)y(x), where the coefficients (c(sub i)(x))i = 0 to i = infinity do not depend on n, for the generalized Jacobi polynomials found by T.H. Koornwinder in 1984 and for generalized Laguerre polynomials which are orthogonal with respect to an inner product of Sobolev type. A method is provided which makes use of computer algebra packages like Maple and Mathematica, and some preliminary results are given. (Copyright (c) 1991 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)