On Complex Multiplicative Integration

Agamirza E. Bashirov and; Mustafa Riza

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arXiv · 1307.8293

On Complex Multiplicative Integration

Agamirza E. Bashirov and·Mustafa Riza

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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.

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Agamirza E. Bashirov and, Mustafa Riza. 2013-07-31. On Complex Multiplicative Integration. https://arxiv.org/abs/1307.8293

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