Multivector functions

AbstractIn a previous paper [1], the fundamentals of differential and integral calculus on Euclidean n-space were expressed in terms of multivector algebra. The theory is used here to derive some powerful theorems which generalize well-known theorems of potential theory and the theory of functions of a complex variable. Analytic multivector functions on εn are defined and shown to be appropriate generalizations of analytic functions of a complex variable. Some of their basic properties are pointed out. These results have important applications to physics which will be discussed in detail elsewhere