Abstract
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.
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