Results 1 to 10 of about 1,739,905 (146)
Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
doaj +2 more sources
Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications
Indian Journal of Pure and Applied Mathematics, 2023 Based on the author's abstract: this paper explores the generalized Cassini identities for the weighted generalized Fibonacci sequences, through the associated generalized Fibonacci fundamental system. Some algebraic, combinatorics and analytic properties of these identities are established.
Elen Viviani Pereira Spreafico
exaly +3 more sources
A bijective proof of Cassini's fibonacci identity
Discrete Mathematics, 1986 The authors provide a short combinatorial proof of the identity \(F^ 2_{n+1}-F_{n+2}F_ n=(-1)^{n+1}\), where \(F_ n\) denotes the n-th Fibonacci number.
M. Werman, Doron Zeilberger
exaly +3 more sources
Journal of MathematicsThis study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r-split quaternions and the Horadam sq,r-split quaternions, which ...
İskender Öztürk, Hasan Çakır
doaj +2 more sources
On Some Properties of Bihyperbolic Numbers of The Lucas Type
Communications in Advanced Mathematical Sciences, 2023 To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
doaj +1 more source
Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers.
Emrah Polatlı
doaj +1 more source
On Harmonic Complex Balancing Numbers
Mathematics, 2022 In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini ...
Fatih Yılmaz +2 more
doaj +1 more source
On Hybrid Numbers with Gaussian Leonardo Coefficients
Mathematics, 2023 We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid
Nagihan Kara, Fatih Yilmaz
doaj +1 more source
On Generalized Pell Numbers of Order r ≥ 2
Trends in Computational and Applied Mathematics, 2021 In this paper we investigate the generalized Pell numbers of order r ≥ 2 through the properties of their related fundamental system of generalized Pell numbers.
E. V. Pereira Spreafico, M. Rachidi
doaj +1 more source
One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
doaj +1 more source