International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1867-1882
On a residue of complex functions in the three-dimensional
Euclidean complex vector space
Kralja Petra I br.1, Čačak 32 000, Serbia and Montenegro
Received 2 December 2001
Copyright © 2003 Branko Sarić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the introductory part of this paper, a notion of absolute
integral sums of a complex function, which is more general with
respect to that of an integral and integral sums of ordinary
integral calculus, is defined. Throughout the main part of the
paper, an attempt has been made to generalize, on the basis of
redefining the notion of a complex function residue, some of the
fundamental results of Cauchy's calculus of residues of analytic
functions. The foundation stone of the whole theory is the total
value of an improper integral of complex functions.