On the differentiability of quaternion functions. (English) Zbl 1280.30022

Dzagnidze, Omar

Tbil. Math. J. 5, No. 1, 1-15 (2012).

Summary: 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.

MSC:

30G35

Functions of hypercomplex variables and generalized variables

Keywords:

functions of a qaternionic variable; elementary quaternion functions