Title q-Classical Orthogonal Polynomials: A General Difference Calculus Approach
Authors COSTAS SANTOS, ROBERTO SANTIAGO, Marcellan, F.
External publication Si
Means Acta Appl Math
Scope Article
Nature Científica
JCR Quartile 2
SJR Quartile 3
JCR Impact 0.97900
SJR Impact 0.34900
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-77953616839&doi=10.1007%2fs10440-009-9536-z&partnerID=40&md5=e6d4d58c049ec192937ef1acd83d65cc
Publication date 01/07/2010
ISI 000278572500009
Scopus Id 2-s2.0-77953616839
DOI 10.1007/s10440-009-9536-z
Abstract It is well known that the classical families of orthogonal polynomials are characterized as the polynomial eigenfunctions of a second order homogeneous linear differential/difference hypergeometric operator with polynomial coefficients.\n In this paper we present a study of the classical orthogonal polynomials sequences, in short classical OPS, in a more general framework by using the differential (or difference) calculus and Operator Theory. The Hahn\'s Theorem and a characterization theorem for the q-polynomials which belongs to the q-Askey and Hahn tableaux are proved. Finally, we illustrate our results applying them to some known families of orthogonal q-polynomials.
Keywords Classical orthogonal polynomials; Discrete orthogonal polynomials; q-Polynomials; Characterization theorems; Rodrigues operator
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