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If you search for the definition of analytic and holomorphic functions in books and online, you get crosses between two definitions (one involving taylor series and one differential) I can find no clear consensus on which definition holds for analytic and which for holomorphic.

I know they are mathematically equivalent but I want to know how they where originally defined? (please could you give a reliable source with your answer)

Quantum spaghettification
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    Taylor series definition is the earliest, see First papers on holomorphic functions thread http://hsm.stackexchange.com/questions/2243/first-papers-on-holomorphic-functions?rq=1 – Conifold Jun 23 '15 at 17:44
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    Umberto Bottazzini and Jeremy Gray, Hidden harmony—Geometric fantasies. The rise of complex function theory. Springer, 2013. – Andrés E. Caicedo Jun 24 '15 at 01:28

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