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arXiv · 1112.2073

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

Natig Atakishiyev·Pedro Franco·Decio Levi·Orlando Ragnisco
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Abstract

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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Natig Atakishiyev, Pedro Franco, Decio Levi, Orlando Ragnisco. 2011-12-09. On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials. https://doi.org/10.1088/1751-8113/45/19/195206

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