q-Classical Orthogonal Polynomials: A General Difference Calculus Approach Articles uri icon

publication date

  • July 2010

start page

  • 107

end page

  • 128

issue

  • 1

volume

  • 111

international standard serial number (ISSN)

  • 0167-8019

electronic international standard serial number (EISSN)

  • 1572-9036

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. 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.