, Volume 34, Issue 1-2, pp 132-149
Date: 17 Apr 2013

Discriminants and Functions of the Second Kind of Orthogonal Polynomials

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Abstract

We consider the problem of evaluating discriminants of general orthogonal polynomials. It is shown that for a general class of weight functions, the functions of the second kind and the orthogonal polynomials are linear independent solutions of the same second order differential equation. We derive a linear fourth-order differential equation satisfied by the numerator polynomials and give two additional linear independent solutions.

To Paul Butzer, in Friendship.
Research partially supported by NSF grant DMS-9625459.