Generalized bicomplex numbers

Abstract

In this paper we introduce and study the following generalized numbers: $BF_{n,m}$ - bicomplex Fibonacci numbers; $BL_{n,m}$ - bicomplex Lucas numbers; $BJ_{n,m}$ - bicomplex Jacobsthal numbers and $Bj_{n,m}$ - bicomplex Jacobsthal-Lucas numbers. For $m=2$, these numbers are the well-known bicomplex Fibonacci numbers; bicomplex Lucas numbers; bicomplex Jacobsthal and bicomplex Jacobsthal-Lucas numbers, respectively. Additionally, we introduce convolutions of these numbers.