Symmetric abstract hypergeometric polynomials

Consider an abstract operator L which acts on monomials xn according to Lxn=λnxn+νnxn−2 for λn and νn some coefficients. Let Pn(x) be eigenpolynomials of degree n of L: LPn(x)=λnPn(x). A classification of all the cases for which the polynomials Pn(x) are orthogonal is provided. A general derivation...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-02, Vol.458 (1), p.742-754
Main Authors: Tsujimoto, Satoshi, Vinet, Luc, Yu, Guo-Fu, Zhedanov, Alexei
Format: Article
Language:English
Subjects:
Abstract hypergeometric operator
Nonlinear algebras
Symmetric orthogonal polynomials
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Summary:Consider an abstract operator L which acts on monomials xn according to Lxn=λnxn+νnxn−2 for λn and νn some coefficients. Let Pn(x) be eigenpolynomials of degree n of L: LPn(x)=λnPn(x). A classification of all the cases for which the polynomials Pn(x) are orthogonal is provided. A general derivation of the algebras explaining the bispectrality of the polynomials is given. The resulting algebras prove to be central extensions of the Askey–Wilson algebra and its degenerate cases.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.09.033