sequence of the hyperbolic k-Padovan quaternions (original) (raw)

The sequence of the hyperbolic k-Padovan quaternions

2023

This work introduces the hyperbolic k-Padovan quaternion sequence, performing the process of complexification of linear and recurrent sequences, more specifically of the generalized Padovan sequence. In this sense, there is the study of some properties around this sequence, deepening the investigative mathematical study of these numbers.

The Sequences of the Hyperbolic k-Perrin and k-Leonardo Quaternions

In this article, hyperbolic k-Perrin and k-Leonardo quaternions are defined. In this sense, bulletin, are evaluated as sequences of k-Perrin and k-Leonardo, their respective quaternions and thus the definition of hyperbolic quaternions. Thus, there are some algebraic properties around numbers, generating function, Binet's formula and properties inherent to these numbers.

On hyperbolic k-Pell quaternions sequences

Annales Mathematicae et Informaticae

In this paper we introduce the hyperbolic k-Pell functions and new classes of quaternions associated with this type of functions are presented. In addition, the Binet formulas, generating functions and some properties of these functions and quaternions sequences are studied.

On a Generalization for Quaternion Sequences

arXiv: Rings and Algebras, 2016

In this study, we introduce a new classes of quaternion numbers. We show that this new classes quaternion numbers include all of quaternion numbers such as Fibonacci, Lucas, Pell, Jacobsthal, Pell-Lucas, Jacobsthal-Lucas quaternions have been studied by many authors. Moreover, for this newly defined quaternion numbers we give the generating function, norm value, Cassini identity, summation formula and their some properties.

On a Special Quaternionic Sequence

Universal Journal of Applied Mathematics, 2018

In this study, we investigate Fibonacci quaternions and their some important properties. Then, we define a special sequence using the elements of the Fibonacci quaternion sequence. Furthermore, we calculate the autocorrelation, right and left periodic autocorrelation values by using the elements of the newly defined sequence.

Hyperbolic k-Fibonacci Quaternions

Journal of Computer Science & Computational Mathematics, 2019

In this paper, hyperbolic k-Fibonacci quaternions are defined. Also, some algebraic properties of hyperbolic k-Fibonacci quaternions which are connected with hyperbolic numbers and k-Fibonacci numbers are investigated. Furthermore, d'Ocagne's identity, the Honsberger identity, Binet's formula, Cassini's identity and Catalan's identity for these quaternions are given.

On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions

DergiPark (Istanbul University), 2022

In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions. Afterward, we derive the Binet-like formulas and their generating functions. Moreover, we provide some binomial sums, Honsberger-like, d'Ocagne-like, Catalan-like, and Cassini-like identities of the hyperbolic Leonardo quaternions and hyperbolic Francois quaternions that allow an understanding of the quaternions' properties and their relation to the Francois sequence and Leonardo sequence. Finally, considering the results presented in this study, we discuss the need for further research in this field.

Circular-hyperbolic Fibonacci quaternions

Notes on Number Theory and Discrete Mathematics, 2020

In this paper, circular-hyperbolic Fibonacci numbers and quaternions are defined. Also, some algebraic properties of circular-hyperbolic Fibonacci numbers and quaternions which are connected with circular-hyperbolic numbers and Fibonacci numbers are investigated.

On a Generalization for Tribonacci Quaternions

Mediterranean Journal of Mathematics

Let Vn denote the third order linear recursive sequence defined by the initial values V 0 , V 1 and V 2 and the recursion Vn = rV n−1 +sV n−2 +tV n−3 if n ≥ 3, where r, s, and t are real constants. The {Vn} n≥0 are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when r = s = t = 1 and to the 3-bonacci numbers when r = s = 1 and t = 0. In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Tribonacci, Padovan, Narayana and Third order Jacobsthal quaternion sequences. We obtained the Binet formula, summation formula and the norm value for this new quaternion sequence.

On a generalization for fibonacci quaternions

Chaos, Solitons & Fractals, 2017

In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas quaternion sequences. We obtained the Binet formula and calculated the Cassini identity, summation formula and the norm value for this new quaternion sequence.