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The fourth-order difference equation satisfied by the associated orthogonal polynomials of the \(\Delta\)-Laguerre-Hahn class. (English) Zbl 0948.65140

The authors present an algorithm which enables to write the general fourth-order difference equation satisfied by the associated orthogonal polynomials of any integer order of the \(\Delta\)-Laguerre-Hahn class, by using the \(D_\omega\)-Riccati difference equation satisfied by the Stieltjes function of a linear functional.

MSC:

65Q05 Numerical methods for functional equations (MSC2000)
39A10 Additive difference equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

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References:

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