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.