International Journal of Difference Equations
  • Year: 2006
  • Volume: 1
  • Issue: 2

Discrete q Hermite Polynomials are Linked by the Integral and Finite Fourier Transforms

  • Author:
  • Metin Arik1, Natig M. Atakishiyev2, Juvenal P. Rueda2
  • Total Page Count: 10
  • Page Number: 195 to 204

1Department of Physics, Boğaziçi University, 34342 Bebek, Istanbul, Turkey.

2Instituto de Matem´aticas, UNAM, CP 62210 Cuernavaca, Morelos, M´exico.

AMS subject classification: 33D45, 42A38.

Abstract

It is shown that the classical Fourier integral transform links the discrete q-Hermite polynomials hn (x; q) of type I and (x; q) of type II. This Fourier integral transform is then used to prove that the same two q-families of polynomials are also interrelated by the finite Fourier transform.

Keywords

Finite Fourier transform, classical Fourier integral transform, discrete q-Hermite polynomial, Hermite functions