Continued Fractions: Analytic Theory and Applications

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Summary

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

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Introduction
Elementary Properties of Continued Fractions
Continued Fractions
Convergence of Continued Fractions
Methods for Representing Analytic Functions by Continued Fractions
Representations of Analytic Functions by Continued Fractions
Types of Corresponding Continued Fractions and Related Algorithms
Truncation-Error Analysis
Asymptotic Expansions and Moment Problems
Numerical Stability in Evaluating Continued Fractions
Application of Continued Fractions to Birth-Death Processes
Miscellaneous Results
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