Results in Mathematics

, Volume 34, Issue 1–2, pp 132–149 | Cite as

Discriminants and Functions of the Second Kind of Orthogonal Polynomials

Research article

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.

1991 Mathematics Subject Classification

42C05 33C45 

Key words and phrases

Discriminants orthogonal polynomials zeros functions of the second kind recurrence relations differential equations raising and lowering operators finite dimensional Lie algebras numerator polynomials 

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South Florida TampaFloridaUSA

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