Calculus with a Quaternionic Variable

Details Calculus with a Quaternionic Variable Calculus with a Quaternionic Variable

2008-12-05

arxiv.org/abs/0812.1185v1

J. Math. Phys. 50, 013523 (2009)

Mathematics

Functional Analysis

16 pages

Scientific paper

10.1063/1.3058642

Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses obstacles for the usual manipulations of calculus; but we show in this paper how many of those obstacles can be overcome. 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*). This advance in the differential calculus for quaternionic variables also leads us to some progress in studying integration.

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