MMN-2832
Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials
H. M. Srivastava; Naim Tuglu; Mirac Cetin;Abstract
In the present paper, we introduce new families of the $q$-Fibonacci
and $q$-Lucas polynomials, which are represented here as the incomplete
$q$-Fibonacci polynomials $F_{n}^{k}\left(x,s,q\right)$ and the incomplete
$q$-Lucas polynomials $L_{n}^{k}\left(x,s,q\right)$, respectively.
These polynomials provide the $q$-analogues of the incomplete Fibonacci
and Lucas numbers. We give several properties and generating functions
of each of these families $q$-polynomials.
We also point out the fact that the results
for the $q$-analogues which we consider
in this article for $0 < q < 1$ can easily be translated into the
corresponding results for the $(p,q)$-analogues (with $0 < q < p \leqq 1$)
by applying some obvious parametric variations, the additional
parameter $p$ being redundant.
Vol. 20 (2019), No. 1, pp. 511-524
DOI: 10.18514/MMN.2019.2832