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 -Fibonacci polynomials and -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 -extensions of classical Hermite polynomials. We show that both of these -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}
}