Thursday, March 15, 2012

1112.2073 (Natig Atakishiyev et al.)

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

Natig Atakishiyev, Pedro Franco, Decio Levi, Orlando Ragnisco
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.
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