English

On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials

Mathematical Physics 2015-06-03 v2 Classical Analysis and ODEs math.MP

Abstract

We study in detail two families of qq-Fibonacci polynomials and qq-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel qq-extensions of classical Hermite polynomials. We show that both of these qq-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform.

Keywords

Cite

@article{arxiv.1112.2073,
  title  = {On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials},
  author = {Natig Atakishiyev and Pedro Franco and Decio Levi and Orlando Ragnisco},
  journal= {arXiv preprint arXiv:1112.2073},
  year   = {2015}
}