A generalization of a Cullen's Integral Theorem for the quaternions

TL;DR

This paper extends Cullen's integral theorem from analytic intrinsic quaternionic functions to a broader class of quaternionic functions, enhancing the theorem's applicability.

Contribution

It generalizes Cullen's integral theorem to a larger class of quaternionic functions, broadening its theoretical scope.

Findings

The integral theorem holds for a wider class of quaternionic functions.

The proof extends the original theorem's validity beyond analytic intrinsic functions.

The result enhances the theoretical framework of quaternionic analysis.

Abstract

We discuss the proof of a certain integral theorem obtained by C. G. Cullen, originally stated on the class of the analytic intrinsic functions on the quaternions. It is shown that this integral theorem is true for a larger class of quaternionic functions.