A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem

Abstract

A new root and ratio test for bicomplex power series produces the bicomplex extension theorem, where any complex power series with positive radius of convergence R extends, via a simple change of the complex domain variable z to the bicomplex variable , to a bicomplex function analytic in a four real-dimensional ball with the same positive radius R. In this way, any complex-analytic function has a natural extension to a bicomplex-analytic function.