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arXiv · 0812.1185

Calculus with a Quaternionic Variable

Charles Schwartz
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Abstract

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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Charles Schwartz. 2008-12-05. Calculus with a Quaternionic Variable. https://doi.org/10.1063/1.3058642

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