Dual-Gaussian Pell and Pell-Lucas numbers

Abstract

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.