Hyperderivatives in Clifford Analysis and Some Applications to the Cliffordian Cauchy-type Integrals
We introduce the notion of the derivative as the limit of a quotient where the numerator and the denominator represent a kind of the “increments” of a function and of the independent variable respectively. The directional derivative is introduced where a direction means a hyperplane in ℝm+1 for a Clifford algebra Cl o,m. The latter applies for obtaining a formula showing how to exchange the integral sign and the hyperderivative of the Cliffordian Cauchy-type integral as a hyperholomorphic function.
KeywordsHyperderivative m-dimensional directional hyperderivative Cliffordian Cauchy-type integrals
Mathematics Subject Classification (2000)Primary 30G35 Secondary 32A10
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