3-Parameter Generalized Quaternions

Şentürk, Tuncay Deniz; Ünal, Zafer

doi:10.1007/s40315-022-00451-7

Cited by 7 publications

(1 citation statement)

References 11 publications

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“…Hence, the -parameter generalized quaternion is the generalization of the others. 2-parameter generalized quaternion [14][15][16][17] 3-parameter generalized quaternion [18] The idea of generalizing quaternions whose components are special integer sequences such as Fibonacci, Lucas, Leonardo and so on has been one of the aims of researchers, [19][20][21][22][23]. In this paper, we answer the question whether it is possible to extend the Leonardosequence via 3-parameter generalized quaternion, which the 3-parameter generalized quaternion units would satisfy the multiplication rules listed in Table .…”

Section: Introduction and Fundamentalsmentioning

confidence: 99%

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

SAÇLI

2024

J. Sci. Arts

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In this article, 3-parameter generalized quaternionic Leonardo p-sequence which is a quaternion generalization of the Leonardo p-sequence is presented. Several properties are examined by means of their homogeneous and non-homogeneous recursive relations. According to the special cases of 3-parameter λ_(i ∈ \{1,2,3\}) and p, all the results given in paper are reducible to all quaternions mentioned in this paper.

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Section: Introduction and Fundamentalsmentioning

confidence: 99%

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

SAÇLI

2024

J. Sci. Arts

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On 3-parameter quaternions with higher order generalized Fibonacci numbers components

Kızılateş,

Kibar

2024

J Anal

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The non-de moivre formula for calculating the power of 3-parameter generalized quaternions

Deng,

Tang

2024

J. Phys.: Conf. Ser.

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In this article, a recursive formula is obtained by using the simplified substitution of the 3-parameter generalized quaternion left matrix representation. Based on it, the direct formula of nth power calculation including real quaternions, split quaternions, split semi-quaternions, and 1/4-quaternions, is derived, which is more universal to solve the problem of inconvenient calculation with the De Moivres formula when the power n is large. Finally, the correctness of the obtained results is verified by two examples.

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3-Parameter Generalized Quaternions

Cited by 7 publications

References 11 publications

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

On 3-parameter quaternions with higher order generalized Fibonacci numbers components

The non-de moivre formula for calculating the power of 3-parameter generalized quaternions

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