Differentiable functions of quaternion variables

Details Differentiable functions of quaternion variables Differentiable functions of quaternion variables

2002-09-13

arxiv.org/abs/math/0209166v1

Mathematics

Complex Variables

48 pages, Latex

Scientific paper

We 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 quaternion 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.

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