(p,q)-Fibonacci and (p,q)-Lucas sums by the derivatives of some polynomials

Fibonacci and Lucas Sums by Matrix Methods

The Fibonacci sequence {Fn} is defined by the recurrence relation Fn = Fn−1+ Fn−2, for n ≥ 2 with F0 = 0 and F1 = 1. The Lucas sequence {Ln} , considered as a companion to Fibonacci sequence, is defined recursively by Ln = Ln−1 + Ln−2, for n ≥ 2 with L0 = 2 and L1 = 1. It is well known that F−n = (−1)Fn and L−n = (−1)Ln, for every n ∈ Z. For more detailed information see [9],[10]. This paper pr...

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

On Some Properties of Bivariate Fibonacci and Lucas Polynomials

In this paper we generalize to bivariate Fibonacci and Lucas polynomials, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate bases are families of integers satisfying remarkable recurrence relations.

On some properties on bivariate Fibonacci and Lucas polynomials

In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.

Some Formulae for Bivariate Fibonacci and Lucas Polynomials

We derive a collection of identities for bivariate Fibonacci and Lu-cas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables x and y are replaced by polynomials. A wealth of combinatorial identities can be obtained for selected values of the variables.