ON COMPLEX MULTIPLICATIVE INTEGRATION
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Isik University
2017-06-01
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| Series: | TWMS Journal of Applied and Engineering Mathematics |
| Subjects: | |
| Online Access: | http://jaem.isikun.edu.tr/web/index.php/current/93-vol7no1/281-on-complex-multiplicative-integration |
| Summary: | 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 multivalued function. Some basic properties of this integral are considered. In particular, it is proved that this integral and the complex multiplicative derivative are bonded in a kind of fundamental theorem. |
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| ISSN: | 2146-1147 2146-1147 |