Related papers: Dual Fibonacci Quaternions
We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of Bernoulli polynomials, making use of the connection between…
By expressing Fibonacci and Lucas numbers in terms of the powers of the golden ratio, $\alpha=(1+\sqrt 5)/2$ and its inverse, $\beta=-1/\alpha=(1-\sqrt 5)/2$, a multitude of Fibonacci and Lucas identities have been developed in the…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this paper we generalize identities from Fibonacci numbers and…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence…
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.
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
In this work, we define a more general family of polynomials in several variables satisfying a linear recurrence relation. Then we provide explicit formulas and determinantal expressions. Finally, we apply these results to recurrent…
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.
The aim of this work is to consider the bicomplex third-order Jacobsthal quaternions and to present some properties involving this sequence, including the Binet-style formulae and the generating functions. Furthermore, Cassini's identity…
In this paper, we define the incomplete h(x)-Fibonacci and h(x)-Lucas polynomials, we study recurrence relations and some properties of these polynomials
We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.
Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contained approach to some bivariate analogs.
We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the…
In this paper, we consider the generalized Fibonacci quaternion which is the Horadam quaternion sequence. Then we used the Binet's formula to show some properties of the Horadam quaternion. We get some generalized identities of the Horadam…
In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.
We study the Fibonacci and Lucas numbers and demonstrate how identities can be constructed by investigating trivalent graphs and splitting fields.
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
In this paper we present two families of Fibonacci-Lucas identities, with the Sury's identity being the best known representative of one of the families. While these results can be proved by means of the basic identity relating Fibonacci…