Gaussian-hyperbolic Numbers Containing Pell and Pell-Lucas Numbers

Abstract

In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-hyperbolic Pell and Pell-Lucas numbers. We also give negaGaussian-hyperbolic Pell and Pell-Lucas numbers. More-over, we obtain the Binet’s formula, generating function formula, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for these new type numbers. Some algebraic proporties of Gaussian-hyperbolic Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix repre-sentation of Gaussian-hyperbolic Pell and Pell-Lucas number.