Results in Mathematics

, Volume 34, Issue 1, pp 132–149

Discriminants and Functions of the Second Kind of Orthogonal Polynomials

Research article

DOI: 10.1007/BF03322044

Cite this article as:
Ismail, M.E.H. Results. Math. (1998) 34: 132. doi:10.1007/BF03322044


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


Key words and phrases

Discriminantsorthogonal polynomialszerosfunctions of the second kindrecurrence relationsdifferential equationsraising and lowering operatorsfinite dimensional Lie algebrasnumerator polynomials

Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South Florida TampaFloridaUSA