Some beautiful q-analogues of Fibonacci and Lucas polynomials

2011/04/14 by Johann Cigler, Cigler, Johann · 3 citations
Mathematics · Physics and Astronomy · #05-02 #05A30 #11B39 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO)

paper · pdf · doi:10.48550/arxiv.1104.2699

openalex publication_date 2011/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

Citations

• An Infinite Family of Engel Expansions of Rogers–Ramanujan Type

Cited by

• A simple approach to q-Chebyshev polynomials
• A bivariate version of the spread polynomials
• Continuous q-Hermite polynomials: An elementary approach

Related

• Some elementary aspects of q-Fibonacci and q-Lucas polynomials
• A simple approach to q-Chebyshev polynomials
• q-Fibonacci polynomials and q-Genocchi numbers
• Some remarks on generalized Fibonacci and Lucas polynomials
• Some conjectures about q-Fibonacci polynomials