Some Appell-type orthogonal polynomials on lattices

2023/01/17 by D. Mbouna, A. Suzuki, Mbouna, D. +1
Mathematics · #Advanced Mathematical Identities #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2301.06728

openalex publication_date 2023/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate on some Appel-type orthogonal polynomial sequences on q-quadratic lattices and we provide some entire new characterizations of the Al-Salam Chihara polynomials (including the Rogers q-Hermite polynomials). The corresponding forms are well described. The proposed method can be applied to similar and to more general problems involving the Askey-Wilson and the Averaging operators, in order to obtain new characterization theorems for classical and semiclassical orthogonal polynomials on lattices.

Related

• Characterization of certain sequences of q-polynomials
• A characterization of the Rogers q-Hermite polynomials
• Discrete orthogonality of the polynomial sequences in the q-Askey scheme
• Characterization of Orthogonal Polynomials on lattices
• A characterization of continuous q-Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials