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Limit relations between \(q\)-Krall type orthogonal polynomials. (English) Zbl 1096.33011
In this paper the authors continue the work started by R. Álvarez-Nodarse and J. Petronilho, [“On the Krall-type discrete polynomials”, J. Math. Anal. Appl. 295, No. 1, 55–69 (2004; Zbl 1051.33006)] and study several families of \(q\)- Krall type orthogonal polynomials. In particular, they obtain the limits of the \(q\)-Krall type polynomials in the \(q\)-Hahn tableau. In such a way the limit relations among the Krall-type families are established. In the paper under review the authors start their presentation with some preliminaries and the basic parameters of the families considered in this work. In particular, they include the explicit values for the kernels of the corresponding \(q\)-classical polynomials in terms of the polynomials and their \(q\)-derivatives. Then the \(q\)-Krall type orthogonal polynomials are defined and some algebraic properties are deduced for these new families. Finally, the limits of the modified polynomials of the examples considered in the paper are established.

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33C47 Other special orthogonal polynomials and functions
33E30 Other functions coming from differential, difference and integral equations
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