Definition talk:Analytic Function/Complex Plane

I am quite sure this definition is more usually called "Holomorphic", and the one with power series "Analytic". These coincide for univariate complex analysis but in the multivariate case they differ - let alone more general Riemann surfaces. --Lord_Farin (talk) 08:10, 31 January 2013 (UTC)


 * This is indeed true. However, most sources on univariate complex analysis use the word "analytic" instead of holomorphic (at least, most of the sources on the net that I've read). I haven't studied multivariate complex analysis, so I can't write anything about that. Feel free to add an explanation to the page. --Anghel (talk) 16:56, 31 January 2013 (UTC)


 * But then what is the power series def. called? Nothing? That seems lacking. I will try to put in €0.02 later tonight. --Lord_Farin (talk) 18:35, 31 January 2013 (UTC)

We might also want to include what it means to be analytic/holomorphic in a set that is not open. (Currently there are no conditions on $D$, while the definition linked to supposes $D$ is open.) --barto (talk) 15:32, 23 January 2017 (EST)


 * If the differences between open and non-open that require the definitions to be fundamentally different, we need to be careful and distinguish between them -- whether as an "also defined as" section or specifically to establish separate pages to draw that difference. As I say, the most difficult part of this area is to decide upon a consistent approach, and to make sure we document the different approaches in those all-important side-notes. --prime mover (talk) 16:05, 23 January 2017 (EST)