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 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 H-derivatives.

Tbilisi Mathematical Journal, Vol. 5(1) (2012), pp. 1-15