Book recommendations - complex analysis

I need a book that's semi-introductory (advanced undergrad to beginning graduate level, if possible) on complex analysis, particularly one that covers power series well, but should be fairly general.

I currently have "elementary real and complex analysis" by Georgi Shilov and while it's not bad, it's not my favorite, either. Also it seems the primary focus of the book is real analysis and the complex analysis is just a side topic almost.

I am hoping perhaps for something rigourous but does not assume terribly much prerequisite knowledge, a little prior complex or real analysis perhaps.

Well, Ahlfors would be the standard choice.

H. Cartan has a complex analysis book, and though I have not yet read it, one would assume that anything written by someone of that level of mathematical capability would be good.
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Science Advisor
I like "Invitation to Complex Analysis" by Ralph Boas. It's somewhat newer than either Ahlfors or Brown and Churchill.
"Visual Complex Analysis" by Tristan Needham is beautiful :tongue: Perhaps because I am more interested in the geometric aspect.


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h. cartan's book is the best reference for the power series approach.

einar hille is also good. ahlfors is indeed standard, but not the easiest read, and not enough excercises.

my favorite is cartan, and he begins with a beautiful treatment of formal power series, almost uniquely among complex analysis books.

and it is also one of the cheapest books, being now a dover paperback.

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