Acta Applicandae Mathematicae

, Volume 111, Issue 1, pp 107–128

q-Classical Orthogonal Polynomials: A General Difference Calculus Approach


DOI: 10.1007/s10440-009-9536-z

Cite this article as:
Costas-Santos, R.S. & Marcellán, F. Acta Appl Math (2010) 111: 107. doi:10.1007/s10440-009-9536-z


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.

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.


Classical orthogonal polynomials Discrete orthogonal polynomials q-Polynomials Characterization theorems Rodrigues operator 

Mathematics Subject Classification (2000)

33C45 33D45 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain