Reference for the theory of analytic functions

Question

Question: Are there any good references for a theory on analytic functions?

Lagrange attempted to develop analysis from this vantage point. Are there any texts that take a similar approach but, address the subject more generally?

Answer 1

For anyone who may be looking for references, the theory of complex analytic functions is covered very well in Analytic Function Theory Volumes I and II by Einar Hille. He includes a lot of motivation to the subject but doesn't skim on the details. There are probably adequate texts for the theory of real analytic functions but, I'm sated with the complex case.

Answer 2

Andrew Gleason took convergent power series as the entry point in his Fundamentals of Abstract Analysis . See http://www.amazon.com/Fundamentals-Abstract-Analysis-Andrew-Gleason/dp/0867202092 . There's a review here: http://www.jstor.org/discover/10.2307/2317164?uid=3739256&uid=2129&uid=2&uid=70&uid=4&sid=21106704524253.

The focus isn't on complex analytic functions - if that's what you want this isn't the answer you want.