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Research Article Open access CC BY 4.0

Gaussian-Hybrid Numbers Obtained From Pell and Pell-Lucas Sequences

Hasan Gökbaş

Journal of Advances in Mathematics and Computer Science · pp. 1–9 · Published 2 Dec 2022

10.9734/jamcs/2022/v37i111719

Abstract

In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-hybrid Pell and Pell-Lucas numbers. We also give negaGaussian-hybrid Pell and Pell-Lucas numbers, the characteristic number and the type number of Gaussian-hybrid 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 formula, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for the Gaussian-hybrid Pell and Pell-Lucas numbers. Some algebraic proporties of Gaussian-hybrid Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix representation of Gaussian-hybrid Pell and Pell-Lucas numbers.

Gaussian-hybrid number Gaussian-hybrid Pell number Gaussian-hybrid Pell-Lucas number

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