Discriminants and Functions of the Second Kind of Orthogonal Polynomials
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- 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.