Convergence of Taylor Series of real normed division algebras

TL;DR

This paper extends classical convergence theorems to quaternionic and octonionic functions, providing new methods to compute their series convergence radii using advanced operators.

Contribution

It introduces novel convergence criteria and extends fundamental theorems to hyperholomorphic and analytic functions in quaternionic and octonionic analysis.

Findings

New formulas for radius of convergence in quaternionic and octonion analysis

Extension of Cauchy-Hadamard and Abel theorems to hypercomplex functions

Application of Fueter and Moisil-Theodoresco operators in convergence analysis

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.