Continued Fractions : Analytic Theory and Applications
This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.
- Electronic book text
- 11 May 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
Table of contents
1. Introduction; 2. Elementary Properties of Continued Fractions; 3. Continued Fractions; 4. Convergence of Continued Fractions; 5. Methods for Representing Analytic Functions by Continued Fractions; 6. Representations of Analytic Functions by Continued Fractions; 7. Types of Corresponding Continued Fractions and Related Algorithms; 8. Truncation-Error Analysis; 9. Asymptotic Expansions and Moment Problems; 10. Numerical Stability in Evaluating Continued Fractions; 11. Application of Continued Fractions to Birth-Death Processes; 12. Miscellaneous Results.
Review of the hardback: 'The first comprehensive and self-contained exposition of the analytic theory of continued fractions in over twenty years'. American Mathematical Monthly