相关论文: Some elementary aspects of q-Fibonacci and q-Lucas…

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

It is shown that some q-analogues of the Fibonacci and Lucas polynomials lead to q-analogues of the Chebyshev polynomials which retain most of their elementary properties.

Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.

We derive a collection of identities for bivariate Fibonacci and Lucas 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…

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…

This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.

We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in…

We evaluate various binomial sums involving the powers of Fibonacci and Lucas numbers.

We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any…

We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.

In the paper, we define the $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions, respectively. Then, we give some algebraic properties of $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions.

We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.

In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.

Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.

In this paper, we introduce relations between binomial sums involving (generalized) Fibonacci and Lucas numbers, and different kinds of binomial coefficients. We also present some relations between sums with two and three binomial…

Using generating functions, we derive many identities involving balancing and Lucas-balancing polynomials. By relating these polynomials to Chebyshev polynomials of the first and second kind, and Fibonacci and Lucas numbers, we offer some…

We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.

The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are…

In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.