The algebra of difference operators associated to Meixner type polynomials

• Published in: Integral transforms and special functions Vol. 34; no. 7; pp. 503 - 521
• Main Authors: Durán, Antonio J., Rueda, Mónica
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03-07-2023; Taylor & Francis Ltd
• Subjects: algebra of difference operators; bispectral orthogonal polynomials; Eigenvectors; Finite differences; Meixner polynomials; Operators (mathematics); Orthogonal polynomials; Polynomials
• ISSN: 1065-2469; 1476-8291
• DOI: 10.1080/10652469.2022.2155642

Meixner type polynomials
are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials
and
. They are eigenfunctions of higher-order difference operators but only for a careful choice of the polynomials
and
, the sequence
is orthogonal with respect to a measure. Under mild assumptions, we characterize in this paper the algebra formed by all difference operators with respect to which the family of Meixner type polynomials
are eigenfunctions.