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In the present paper we extend the concepts of multiplicative de- rivative and integral to complex-valued functions of complex variable. Some drawbacks, arising with these concepts in the real case, are explained satis- factorily. Properties of complex multiplicative derivatives and integrals are studied. In particular, the fundamental theorem of complex multiplicative calculus, relating these concepts, is proved. It is shown that complex multi- plicative calculus is not just another realization of the ordinary calculus. In particular, the Cauchy formula of complex calculus disappears in multiplicative complex calculus.Comment: original researc

Topics:
Mathematics - Complex Variables, 30A99

Year: 2011

OAI identifier:
oai:arXiv.org:1103.1462

Provided by:
arXiv.org e-Print Archive

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