Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials Article Swipe

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Fibonacci number Mathematics Fibonacci polynomials Lucas number Combinatorics Discrete mathematics Difference polynomials Orthogonal polynomials

H. M. Srivastava , Naim Tuğlu , Miraç Çetin ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.18514/mmn.2019.2832 · OA: W2964844917

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 k n .x;s; q/ and the incomplete q-Lucas polynomials L k n .x;s; q/, 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 5 1) by applying some obvious parametric variations, the additional parameter p being redundant.