On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas   polynomials
  We study in detail two families of $q$-Fibonacci polynomials and $q$-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 $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform. 
Natig Atakishiyev, Pedro Franco, Decio Levi and Orlando Ragnisco
math-ph math.CA math.MP