Description

This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods. This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods. This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods. This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods. 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