ON COMPLEX MULTIPLICATIVE INTEGRATION

AGAMIRZA E. BASHIROV, SAJEDEH NOROZPOUR

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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 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.

Keywords

complex calculus, complex integral, multiplicative calculus, fundamental theorem of calculus.