In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas we define tessarines tessarines. We obtain Binet formulae, D’ocagnes identity Cassini for these also give of negatessarines new vector which are called tessarine vector.

We have investigated new Pauli Fibonacci and Lucas quaternions by taking the components of these as Gaussian numbers, respectively. calculated some basic identities for quaternions. Later, generating functions Binet formulas are obtained Furthermore, Honsberger’s identity, Catalan’s Cassini’s been given

Abstract By means of the telescoping method, several summation formulae are established for arctangent function with its argument being Pell and Pell–Lucas polynomials. Numerous infinite series identities involving Fibonacci Lucas numbers included as particular cases.

In this paper, we consider the generalized Fibonacci and Pell Sequences and then show the relationships between the generalized Fibonacci and Pell sequences, and the Hessenberg permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Pell Sequence, fPng ; is de…ned by the recurrence...

In this paper, we prove several identities involving linear combinations of convolutions the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes second-order linearly recurrent sequences with constant coefficients. As a consequence, obtain as special cases many relating exactly four amongst Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, Jacobsthal–Luc...

In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Pell Narayana simultaneously. We prove some identities generalize well-known relations for numbers their generalizations. A matrix representation generalized is given, too.

In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, matrix representation quaternions determined. The Q_k defined numbers given By means of another matrices, several identities are also obtained.

In the present paper, we first study Gaussian Leonardo numbers and hybrid numbers. We give some new results for numbers, including relations with Fibonacci Lucas also For proofs, use symmetric antisymmetric properties of Then, introduce polynomials, which can be considered as a generalization After that, using polynomials coefficients instead real in Moreover, obtain recurrence relations, gener...

In this paper, we investigate Fibonacci polynomials as complex hyperbolic functions. We examine the roots of these polynomials. Also, give some exciting identities about images under another member class. Finally, obtain excellent relationships between and modular group, Hecke groups generalized with geometric interpretations.