Tbilisi Mathematical Journal

On the Differentiability of Quaternion Functions

Omar Dzagnidze

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

Article information

Tbilisi Math. J., Volume 5, Issue 1 (2012), 1-15.

Received: 3 May 2011
Revised: 27 March 2012
Accepted: 2 April 2012
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30G35: Functions of hypercomplex variables and generalized variables
Secondary: 30A05: Monogenic properties of complex functions (including polygenic and areolar monogenic functions) 30B10: Power series (including lacunary series)

Quaternion $\mathbb{H}$-derivative elementary quaternion functions


Dzagnidze, Omar. On the Differentiability of Quaternion Functions. Tbilisi Math. J. 5 (2012), no. 1, 1--15. https://projecteuclid.org/euclid.tbilisi/1528768885

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