Gaussian Fibonacci and Gaussian Lucas \(p\)-Numbers

Abstract

In this paper, we define and study the Gaussian Fibonacci and Gaussian Lucas \(p\)-numbers. We give generating functions, Binet formulas, explicit formulas, matrix representations, and sums of Gaussian Fibonacci \(p\)-numbers by matrix methods. For \(p = 1\), these Gaussian Fibonacci and Gaussian Lucas \(p\)-numbers reduce to the Gaussian Fibonacci and the Gaussian Lucas numbers.