Continued Fractions with Applications

L. Lorentzen (Author), H. Waadeland (Author)

9780444892652, Elsevier Science

Hardback, published 24 April 1992

616 pages
23.4 x 15.6 x 3.4 cm, 1.04 kg

A. Bultheel
"...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." --Newsletter on Computational and Applied Mathematics

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.

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. Pad&eacute
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.

Subject Areas: Mathematical theory of computation [UYA], Optimization [PBU], Real analysis, real variables [PBKB], Number theory [PBH], Algebra [PBF], Mathematical logic [PBCD]