2000 character limit reached
Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme (2301.00678v3)
Published 2 Jan 2023 in math.CA, hep-th, math-ph, math.MP, and nlin.SI
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.