Generalizations of Rodrigues type formulas for hypergeometric difference equations on nonuniform lattices. (English) Zbl 1453.33014

Summary: By building a second-order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second-order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a ‘generalized’ Rodrigues formula is also established.


33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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