A note on hyperbolic quaternions

Kösal, Işıl Arda

doi:10.32323/ujma.380645

Cited by 6 publications

(1 citation statement)

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“…Thus, Macfarlane defined the hyperbolic quaternions and studied their properties [18]. Recently, these numbers have been examined and studies have been carried out [10,13,24]. The hyperbolic k-Fibonacci and k-Fibonacci-Lucas, hyperbolic k-Jacobsthal and k-Jacobsthal-Lucas quaternions were defined and given some of their properties [10,24].…”

Section: Introductionmentioning

confidence: 99%

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

UYSAL,

KUMARI,

KULOĞLU

et al. 2024

KgJMat

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In this paper, we introduce the hyperbolic k-Mersenne and k-Mersenne-Lucas octonions and investigate their algebraic properties. We give Binet’s formula and present several interrelations and some well-known identities such as Catalan identity, d’Ocagne identity, Vajda identity, generating functions, etc. of these octonions in closed form. Furthermore, we investigate the relations between hyperbolic k-Mersenne octonions and hyperbolic k-Mersenne-Lucas octonions.

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Section: Introductionmentioning

confidence: 99%

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

UYSAL,

KUMARI,

KULOĞLU

et al. 2024

KgJMat

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The matrices of Pauli quaternions, their De Moivre’s and Euler’s formulas

Akbiyik

Yılmaz

2022

Int. J. Geom. Methods Mod. Phys.

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In this paper, we obtain Euler’s and De Moivre’s formulas for the [Formula: see text] matrix representation of Pauli quaternions. Moreover, we provide De Moivre’s formula for the light-like Pauli quaternions. Additionally, we give the [Formula: see text] roots of the matrix representation of Pauli quaternions. Moreover, we exemplify some of the results with illustrative examples to support the main formulas.

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A note on hyperbolic (p,q)-Fibonacci quaternions

Yağmur

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we introduce a new quaternion sequence called hyperbolic (p; q)-Fibonacci quaternions. This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic Pell, hyperbolic k-Pell, hyperbolic Jacobsthal, hyperbolic k-Jacobsthal quaternions. We give generating function and Binet's formula for these quaternions. We also obtain some identities such as d'Ocagne's, Catalan's and Cassini's identities involving hyperbolic (p; q)-Fibonacci quaternions.

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A note on hyperbolic quaternions

Abstract: In this work, we introduce hyperbolic quaternions and their algebraic properties. Moreover, we express Euler's and De Moivre's formulas for hyperbolic quaternions.

Cited by 6 publications

References 8 publications

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

The matrices of Pauli quaternions, their De Moivre’s and Euler’s formulas

A note on hyperbolic (p,q)-Fibonacci quaternions

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