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arXiv · 1701.04179

Symmetric abstract hypergeometric polynomials

Satoshi Tsujimoto·Luc Vinet·Guo-Fu Yu·Alexei Zhedanov
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Abstract

Consider an abstract operator $L$ which acts on monomials $x^n$ according to $L x^n= λ_n x^n + ν_n x^{n-2}$ for $λ_n$ and $ν_n$ some coefficients. Let $P_n(x)$ be eigenpolynomials of degree $n$ of $L$: $L P_n(x) = λ_n P_n(x)$. A classification of all the cases for which the polynomials $P_n(x)$ 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.

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Satoshi Tsujimoto, Luc Vinet, Guo-Fu Yu, Alexei Zhedanov. 2017-01-16. Symmetric abstract hypergeometric polynomials. https://arxiv.org/abs/1701.04179

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