A Note on Bigaussian Pell and Pell-Lucas Numbers

Abstract

In this study, we define a new type of Pell and Pell-Lucas numbers which are called biGaussian Pell and biGaussian Pell-Lucas numbers. We also give the relationship between negabiGaussian Pell and Pell-Lucas numbers and bicomplex Pell and Pell-Lucas numbers. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sums formulas for these new type numbers. Some algebraic proporties of biGaussian Pell and Pell-Lucas numbers which are connected between biGaussian numbers and Pell and Pell-Lucas numbers are investigated. Moreover, we give the matrix representation of biGaussian Pell and Pell-Lucas numbers.

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

“…There are a number of studies in the literature that are concerned with these numbers [6][7][8][9]. Fjelstad and Gal [2] inspected the extensions of the hyperbolic complex numbers to n-dimensions and they gave n-dimensional dual complex numbers in algebra and analysis.…”

Gaussian Quaternions Including Biperiodic Fibonacci and Lucas Numbers

“…There have been many works in literature about this special number sequence. There are many generalizations on this sequence some of which can be seen in (Horadam, 1961;Pand, 1968;George, 1969;Pethe and Phadte, 1992;Falcon and Plaza, 2007;Gökbaş, 2021).…”