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This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.
Any commentary upon the present volume by Professors Jones and Thron on the analytic theory of continued fractions must begin with the remarkable fact that it is the first systematic treatment of the theory of continued fractions in book form for over two decades. As such, it supplants and updates to a large degree the well-known treatise by Oskar Perron which in its various editions dominated the exposition of this theory for over 50 years, a veritable monument of Germanic Griindlichkeit. The fact that Perron's book of 1957 (and its coadjutors by Wall in 1948 and Khovanskii in 1956) has had to wait so long for a successor (and indeed that Perron's book seems never to have been translated into English) raises some significant questions about the role of continued fractions as a focus of contemporary mathematical activity. The study of finite continued fractions, i.e., expressions of the form