Improved Validated Bounds for Taylor Coefficients and for Taylor Remainder Series
Date: 30. 11. 2001
This paper presents methods for the validated computation of bounds for Taylor
coefficients and bounds for Taylor remainder series of analytic functions.
These bounds are derived from modifications of Cauchy's estimate.
The proposed methods have been implemented in mathematical software called
ACETAF. Interval arithmetic is used to restore mathematical rigour to
practical calculations. The performance of ACETAF is demonstrated with
Primary MSC: 30B10 Power series (including lacunary series), 30-04 Explicit machine computation and programs (not the theory of computation or programming)
Keywords: Bounds for Taylor coefficients of analytic functions, complex interval arithmetic, enclosure methods, mathematical software