On Complex Multiplicative Integration
Complex Variables
2013-08-01 v1
Abstract
In the present paper we extend the multiplicative integral to complex-valued functions of complex variable. The main difficulty in this way, that is the multi-valued nature of the complex logarithm, is avoided by division of the interval of integration to a finite number of local intervals, in each of which the complex logarithm can be localized in one of its branches. Interestingly, the complex multiplicative integral became a multi-valued function. Some basic properties of this integral are considered. In particular, it is proved that this integral and the complex multiplicative derivative bonded in a kind of fundamental theorem.
Cite
@article{arxiv.1307.8293,
title = {On Complex Multiplicative Integration},
author = {Agamirza E. Bashirov and and Mustafa Riza},
journal= {arXiv preprint arXiv:1307.8293},
year = {2013}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1103.1462