# Analytic and holomorphic functions, definitions and foundations?

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)

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