A Quaternionic Integration Similar to the Complex One

TL;DR

This paper develops a quaternionic integration theory analogous to complex analysis, extending classical theorems like Cauchy's and Laurent's to the quaternion setting, using a generalized H-plane concept.

Contribution

It introduces a quaternionic integration framework that generalizes complex analysis theorems, including Taylor, Cauchy, and Laurent series, to quaternions.

Findings

Quaternionic integration theory analogous to complex analysis

Extension of classical theorems like Cauchy's and Laurent's to quaternions

Introduction of the H-plane concept for quaternionic analysis

Abstract

The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the notion of a number complex plane, the theory of the quaternionic integration similar to the complex one is built. The complex Taylor Theorem, Cauchy's Theorem, Cauchy's Integral Formula, Laurent's series, Laurent's theorem, and Cauchy's Residue Theorem are directly adapted to the quaternion case.