Differentiable functions of quaternion variables

AbstractWe investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy–Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass' theorem