On the Hyperderivatives of Moisil–Théodoresco Hyperholomorphic Functions
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Any Moisil-Th´eodoresco-hyperholomorphic function is also Fueterhyperholomorphic, but its hyperderivative is always zero, so these functions can be thought of as “constants” for the Fueter operator. It turns out that it is possible to give another kind of hyperderivatives “consistent” with the Moisil- Th´eodoresco operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of two-dimensional directional hyperderivative along a plane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.
KeywordsHyperderivative two-dimensional directional hyperderivative Cauchy-type integrals
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