Convergence of Taylor Series of real normed division algebras

Abstract

We propose a new way to compute the radius of convergence for Quaternionic hyperholomorphic functions and for Octonion analytic functions. We extend the theorem of Cauchy Hadamard and the theorem of Abel on convergence of series to Quaternionic analysis with the Fueter Operator, to Quaternionic analysis with the Moisil Theodoresco operator and to the Octonion analysis with the Fueter operator.