On discrete coherent pairs of measures. Issue 7 (3rd July 2022)

• Record Type: Journal Article
• Authors: Álvarez-Nodarse, R.; Castillo, K.; Mbouna, D.; Petronilho, J.
• Is Part Of: Journal of difference equations and applications. Volume 28:Issue 7(2022)
• Page Start: 853
• Page End: 868
• Publication Date: 2022-07-03
• Subjects: Orthogonal polynomials -- coherent pairs of measures -- semiclassical orthogonal polynomials; 42C05 -- 33C45; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2022.2097870
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : In Castillo and Mbouna [On another extension of coherent pairs of measures, Indag. Math. 31 (2020), pp. 223–234], the concept of π N -coherent pairs of order ( m, k ) with index M is introduced. This definition, implicitly related with the standard derivative operator, automatically leaves out the so-called discrete orthogonal polynomials. The purpose of this note is twofold: first, we use the (discrete) Hahn difference operator and rewrite the known results in this framework; second, as an application, we describe exhaustively the (discrete) self-coherent pairs in the situation whether M = 0, N ≤ 2, and ( m, k ) = ( 1, 0 ) . This is proved by describing in a unified way the classical orthogonal polynomials with respect to Jackson's operator as special or limiting cases of a four parametric family of q -polynomials.