On the Differentiability of Quaternion Functions

Omar Dzagnidze

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arXiv · 1203.5619

On the Differentiability of Quaternion Functions

Omar Dzagnidze

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Abstract

Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show that the elementary quaternion func- tions introduced by Hamilton as well as the quaternion logarithm function possess such a derivative. We conclude by establishing rules for calculating H-derivatives.

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Omar Dzagnidze. 2012-03-26. On the Differentiability of Quaternion Functions. https://arxiv.org/abs/1203.5619

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