Some identities for the generalized Fibonacci polynomials by the Q(x) matrix

2020/12/31 by Chung-Chuan Chen, Chen, Chung-Chuan, Lin-Ling Huang +1
Mathematics · #11B37. 11B39 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B37. #msc:11B39

paper · pdf · doi:10.48550/arxiv.2012.15508

arxiv created 2020/12/31 · arxiv updated 2021/01/01

Abstract

In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci polynomials, Lucas polynomials, Pell polynomials, Pell-Lucas polynomials, Fermat polynomials, Fermat-Lucas polynomials, and so on.

Related

• Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers
• Fibonacci identities from Jordan Identities
• Some remarks on generalized Fibonacci and Lucas polynomials
• Some notes on a Fibonacci-Lucas identity
• Some formulae for bivariate Fibonacci and Lucas polynomials