A generalization of a theorem of Bochner
A theorem of \textit{S.~Bochner} [Über Sturm-Liouvillesche Polynomsysteme, Math. Z. 29, 730--736 (1929; JFM 55.0260.01)] for classifying polynomial solutions to a certain second order differential equation is generalized to the \(q\)-hypergeometric case. To this end, the ordinary differential operators are replaced by the Askey-Wilson divided difference operators. The solutions, which have been Jacobi, Laguerre, and Bessel polynomials in Bochner's case, then turn out to be variants of Askey-Wilson polynomials.
scientific article; zbMATH DE number 2006400