Cauchy_Riemann Equations for Cayley Numbers` Functions

TL;DR

This paper proposes a new approach to defining functions of octonions, addressing the long-standing challenge of developing a satisfactory theory for octave-valued functions, especially considering nonassociativity.

Contribution

It introduces a novel framework inspired by Cauchy-Riemann equations to better understand octonion-valued functions, aiming to fill a theoretical gap.

Findings

Proposes a new set of equations for octonion functions

Addresses nonassociativity in function theory

Lays groundwork for future mathematical development

Abstract

Since the discovery of octonions in 1843 we seem to be still lacking a satisfactory if any theory of octave valued functions satisfactory according to standard requirements or expectation from the side of a theory like a one might look for. Here is a proposal coming back to my twentieth century presentation of a perhaps nonstandard idea hoping to be coping with nonassociativity by an invention.