Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters

We construct new examples of bispectral dual Hahn polynomials, i.e., orthogonal polynomials with respect to certain superposition of Christoffel and Geronimus transforms of the dual Hahn measure and which are also eigenfunctions of a higher order difference operator. The new examples have the novelt...

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Bibliographic Details
Published in:Journal of approximation theory 2022-11, Vol.283, p.105811, Article 105811
Main Author: Durán, Antonio J.
Format: Article
Language:English
Subjects:
Dual Hahn polynomials
Krall discrete polynomials
Orthogonal polynomials
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Summary:We construct new examples of bispectral dual Hahn polynomials, i.e., orthogonal polynomials with respect to certain superposition of Christoffel and Geronimus transforms of the dual Hahn measure and which are also eigenfunctions of a higher order difference operator. The new examples have the novelty that they depend on an arbitrary number of continuous parameters. These are the first examples with this property constructed from the classical discrete families.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2022.105811