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This is a cross-post from MSE.

For my Bachelor's thesis, I am investigating divergent series summation methods. One of those is analytic continuation. There are quite a few books on complex analysis that include a chapter or two on analytic continuation, but I would like to study this phenomenon in more detail. Could you please suggest a book on analytic continuation? Or a book on complex analysis with a heavy focus on analytic continuation?

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Not specifically for analytic continuation, but on the topic of summation methods, there is the nice recent book by Shawyer and Watson, Borel's methods of summability, see here for a few details. – Andrés Caicedo Apr 5 '14 at 16:11

English books are Hardy, Divergent series, and P. Dienes, Taylor series: an introduction to the theory of functions of a complex variable. Dover Publications, Inc., New York, 1957. (The title is somewhat misleading. This is a large book that indeed contains an "introduction to complex variables" but it is also the most comprehensive book in English on analytic continuation). But the best book on my opinion is L. Bieberbach, Analytische Fortsetzung, Springer Berlin, 1955, which is available in German and Russian only. (Russian translation by Evgrafov is better because many mistakes are corrected, and some proofs simplified).

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There is a book on Complex Variables with Physical Applications by Arthur A.Hauser, Jr. is theory and step-by step solutions to 760 problems.Chapter 10 of this book deals at grant extend on Analytic Continuation.

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