Dual-complex k-Pell quaternions

Aydın, Fügen Torunbalcı

doi:10.7546/nntdm.2019.25.3.111-125

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Cited by 3 publications

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“…In 2018, Torunbalcı Aydın introduced dual-complex Pell and Pell-Lucas quaternions [20] (submitted) as follows:…”

Section: Introductionmentioning

confidence: 99%

Dual-complex k-Pell quaternions

Aydın

2018

Preprint

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

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“…In 2018, Torunbalcı Aydın introduced dual-complex Pell and Pell-Lucas quaternions [20] (submitted) as follows:…”

Section: Introductionmentioning

confidence: 99%

Dual-complex k-Pell quaternions

Aydın

2018

Preprint

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Dual-Gaussian Pell and Pell-Lucas numbers

Gökbaş

2022

Cumhuriyet Science Journal

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In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell and Pell-Lucas numbers. Also, some sum ve product properties of Pell and Pell-Lucas numbers are given. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for these new type numbers. Some algebraic proporties of dual-Gaussian Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix representation of dual-Gaussian Pell and Pell-Lucas numbers.

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On a new one-parameter generalization of dual-complex Jacobsthal numbers

Bród

Szynal‐Liana

Włoch

2021

Acta Universitatis Sapientiae, Mathematica

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In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.

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Dual-complex k-Pell quaternions

Cited by 3 publications

References 12 publications

Dual-complex k-Pell quaternions

Dual-complex k-Pell quaternions

Dual-Gaussian Pell and Pell-Lucas numbers

On a new one-parameter generalization of dual-complex Jacobsthal numbers

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