@inproceedings{a44b3badee1b46c68b093bc2277047ea,
title = "Hyperderivatives in Clifford analysis and some applications to the Cliffordian Cauchy-type integrals",
abstract = "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 Cl0,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.",
keywords = "Cliffordian Cauchy-type integrals, Hyperderivative, M-dimensional directional hyperderivative",
author = "Luna-Elizarrar{\'a}s, {M. E.} and Mac{\'i}as-Cede{\~n}o, {M. A.} and M. Shapiro",
note = "Publisher Copyright: {\textcopyright} 2008 Birkh{\"a}user Verlag Basel/Switzerland.; 6th ISAAC Conference on Quaternionic and Clifford Analysis, 2007 ; Conference date: 01-08-2007",
year = "2009",
doi = "10.1007/978-3-7643-9893-4_14",
language = "Ingl{\'e}s",
isbn = "9783764398927",
series = "Trends in Mathematics",
publisher = "Springer International Publishing",
pages = "221--234",
editor = "Irene Sabadini and Michael Shapiro and Frank Sommen",
booktitle = "Hypercomplex Analysis",
}