On the Generalized Leonardo Pisano Octonions

Prasad, Kalika; Mahato, Hrishikesh; Kumari, Munesh; Mohanty, R. K.

doi:10.1007/s40009-023-01291-2

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…İşbilir et al [23] investigated the Pauli-Leonardo quaternions. Some recent developments on Leonardo numbers, their generalizations and interesting properties can be seen in [3,5,[14][15][16][17][18][19]22]. Here we restate some of them.…”

Section: Introductionmentioning

confidence: 99%

On The Generalized Leonardo Quaternions and Associated Spinors

KUMARI,

PRASAD,

MAHATO

et al. 2024

KgJMat

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In this paper, we introduce and study a new family of sequences called the generalized Leonardo spinors by deﬁning a linear correspondence between the generalized Leonardo quaternions and spinors. We start with deﬁning the generalized Leonardo quaternions and then present their some important properties such as Binet type formula, Catalan’s identity, d’Ocagne’s identity, series sums, etc. We give some interrelations of these quaternions with the Fibonacci and Lucas quaternions. Then, we present the generating functions, sum formulae, various well-known identities, etc. for the Leonardo spinors and show their connection with the Fibonacci and Lucas spinors.

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Section: Introductionmentioning

confidence: 99%

On The Generalized Leonardo Quaternions and Associated Spinors

KUMARI,

PRASAD,

MAHATO

et al. 2024

KgJMat

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Algebra of quaternions and octonions involving higher order Mersenne numbers

Kumari,

Prasad,

Mohanta

2024

Proc.Indian Natl. Sci. Acad.

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On the Leonardo Sequence via Pascal-Type Triangles

Halıcı,

Curuk

2024

Journal of Mathematics

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In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers. With the help of the properties obtained in this study, we defined a number sequence containing the new type of Leonardo numbers created by choosing the coefficients from the bicomplex numbers. Furthermore, we gave the relationship of this newly defined sequence with the Fibonacci sequence. We also provided some important identities in the literature provided by the elements of this sequence described in this paper.

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On the Generalized Leonardo Pisano Octonions

Cited by 3 publications

References 15 publications

On The Generalized Leonardo Quaternions and Associated Spinors

On The Generalized Leonardo Quaternions and Associated Spinors

Algebra of quaternions and octonions involving higher order Mersenne numbers

On the Leonardo Sequence via Pascal-Type Triangles

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