IJPAM: Volume 68, No. 1 (2011)

HYPERCOMPLEX GEOMETRIC DERIVATIVE
FROM A CAUCHY-LIKE INTEGRAL FORMULA

M.F. Borges$^1$, A.D. Figueiredo$^2$, J.A. Marão$^3$
$^1$Department of Computing
São Paulo State University - UNESP
São José do Rio Preto Campus
São José do Rio Preto, SP, 15054-000, BRAZIL
e-mail: borges@ibilce.unesp.br
$^{2,3}$Institute of Physics
University of Brasilia - UnB
Brasília, 70919-970, BRAZIL
e-mail: annibal@pq.cnpq.br


Abstract. The derivation and integration of hipercomplex functions have been investigated along the years, see [#!1!#], [#!2!#], [#!3!#]. The main purpose of this brief article is to give a geometrical interpretation for quaternionic derivatives, based on a recent determination of a Cauchy-like formula for quaternions, see [#!14!#].

Received: November 23, 2010

AMS Subject Classification: 30G99, 30E99

Key Words and Phrases: Cauchy integral, hypercomplex geometric derivative, quaternions


Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 1