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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.

Continued fractions. --- Mathematics. --- Theorems. --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Continued fractions --- Convergence --- Engineering & Applied Sciences --- Applied Mathematics --- Convergence. --- Fractions, Continued --- Algebra. --- Mathematical analysis --- Math --- Science --- Functions --- Series --- Processes, Infinite

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This book is aimed at two kinds of readers : firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

Numerical approximation theory --- Continued fractions --- Fractions continues --- Continued fractions. --- Fractions continues.

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Science --- Mathematics --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- analyse (wiskunde) --- functies (wiskunde) --- wetenschap --- informatica --- wetenschappen --- wiskunde --- ingenieurswetenschappen

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Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, namely the Handbook of Mathematical Functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Continued fractions --- Functions, Special --- Mathematical analysis --- Continued fractions. --- Functions, Special. --- Mathematical analysis. --- Computer science. --- Engineering mathematics. --- Engineering. --- Mathematics. --- Fonctions continues --- Fonctions spéciales --- Analyse mathématique --- Informatique --- Mathématiques de l'ingénieur --- wiskunde --- Mathematics --- Fonctions continues. --- Fonctions spéciales. --- Analyse mathématique. --- Informatique. --- Mathématiques de l'ingénieur.