Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers

Year 2023, Volume: 9 Issue: 1, 183 - 189, 06.03.2023

Hasan Gökbaş

https://doi.org/10.28979/jarnas.1110421

Cited By: 1

Abstract

In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Catalan’s identities, Cassini’s identities and some sum formulas for these new type numbers and we investigate some algebraic proporties of these. Furthermore, we give the matrix representation of Gaussian-bihyperbolic Pell and Pell-Lucas numbers.

Keywords

biHyperbolic, Gaussian-bihyperbolic, Gaussian-bihyperbolic Pell, Gaussian-bihyperbolic Pell-Lucas

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