Analytic Functions of a Quaternionic Variable

Details Analytic Functions of a Quaternionic Variable Analytic Functions of a Quaternionic Variable

2008-03-26

arxiv.org/abs/0803.3782v2

Mathematics

Functional Analysis

8 pages; added references and added Appendix B on SU(2)

Scientific paper

Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show how many of those obstacles can be overcome. After a tiny bit of linear algebra we look at the beginnings of differential calculus. The surprising result is that the first order term in the expansion of F(x+delta) is a compact formula involving both F'(x) and [F(x) - F(x*)]/(x-x*).

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