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Some recent results in the analytic theory of continued fractions. (English) Zbl 0679.40003

Nonlinear numerical methods and rational approximation, Proc. Conf., Antwerp/Belgium 1987, Math. Appl., D. Reidel Publ. Co. 43, 299-333 (1988).
[For the entire collection see Zbl 0658.00009.]
This is a well written paper which introduces some of the more recent concepts of analytic continued fractions such as element and value region, right and wrong tails, prevalue region limit region, modified approximants and truncation error estimates and general convergence. Several theorems with examples are given illustrating the computation of continued fractions and finally an application is made of location of zero free region for polynomials satisfying three term linear recurrence relations.
Reviewer: A.Magnus

MSC:

40A15 Convergence and divergence of continued fractions

Citations:

Zbl 0658.00009