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

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.