Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme

Abstract

The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the differential or difference operators. Based on other factorizations, we obtain another type of forward and backward shift relations. Essentially, these shift relations shift only the parameters.

31 pages. The Rodrigues-type formulas, some comments and reference are added. To appear in J. Math. Anal. Appl

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Cited by in corpus (1)

• Some Difference Relations for Orthogonal Polynomials of a Continuous Variable in the Askey Scheme