Mersenne-Lucas hybrid numbers

Özkan, Engi̇n; Uysal, Mi̇ne

doi:10.20948/mathmontis-2021-52-2

Cited by 11 publications

(6 citation statements)

References 16 publications

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“…Moreover, they gave the roots of the matrix representation of hybrid numbers and some results. In [6], the authors described Mersenne-Lucas numbers. Also, they presented the Binet formula, the generating function, several identities.…”

Section: Multiplication Table Of Hybrid Unitsmentioning

confidence: 99%

Generalized k-Order Fibonacci Hybrid Quaternions

Gül

2022

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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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, the matrix representation for generalized k-order Fibonacci hybrid quaternions is determined. The Q_k matrix defined for k-order Fibonacci numbers is given for the generalized k-order Fibonacci hybrid quaternions. By the means of this matrix and another defined matrices, several identities of these quaternions are also obtained.

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Section: Multiplication Table Of Hybrid Unitsmentioning

confidence: 99%

Generalized k-Order Fibonacci Hybrid Quaternions

Gül

2022

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…There have been some studies on hybrid numbers [22][23][24][25][26][27][28]. The product rule for hybrid units is shown in Table 2.…”

Section: Table 1 Multiplication Of Quaternion Unitmentioning

confidence: 99%

Padovan Hybrid Quaternions and Some Properties

Uysal

Özkan

2022

J. Sci. Arts

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“…They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. Mersenne numbers have been studied in the literature and various generalizations such as Mersenne-Lucas, k-Mersenne, k-Mersenne-Lucas have been studied [1,4,6,7,17,22,[25][26][27].…”

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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Mersenne-Lucas hybrid numbers

Cited by 11 publications

References 16 publications

Generalized k-Order Fibonacci Hybrid Quaternions

Generalized k-Order Fibonacci Hybrid Quaternions

Padovan Hybrid Quaternions and Some Properties

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

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