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

Branko Sarić

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.