Continued Fractions – Vol 1: Convergence Theory (2nd Edition) (Atlantis Studies in Mathematics for Engineering and Science) 2nd Edition by Lisa Lorentzen (PDF)

Description

Continued Fractions consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given.This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.

User’s Reviews

Editorial Reviews: Review The authors are leaders in the field, and have a long and productive history working with continued fractions. Indeed, many modern advances in analytic theory of continued fractions can be attributed to their work. The authors are therefore able to bring a deep and rich background to the subject ]] The book is nicely written and a pleasure to read. — Phil Gustafson “Professor of Mathematics”

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