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.

Table of Contents

I. Introductory Examples. II. More Basics. III. Convergence Criteria. IV. Continued Fractions and Three-Term Recurrence Relations. V. Correspondence of Continued Fractions. VI. Hypergeometric Functions. VII. Moments and Orthogonality. VIII. Padé Approximants. IX. Some Applications in Number Theory. X. Zero-free Regions. XI. Digital Filters and Continued Fractions. XII. Applications to Some Differential Equations. Appendix: Some Continued Fraction Expansions. References. Index.


No. of pages:
© 1992
North Holland
eBook ISBN:
Print ISBN:
Print ISBN:

About the authors

L. Lorentzen

Affiliations and Expertise

Division of Mathematical Sciences, University of Trondheim, Norway

H. Waadeland

Affiliations and Expertise

Department of Mathematics and Statistics, University of Trondheim, Norway


@from:A. Bultheel @qu:...ample material to make the reader fall in love with continued fractions... If you are interested in learning about continued fractions, this book should be on the top of your reading list. @source:Newsletter on Computational and Applied Mathematics