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On the Approximation of Irrationals by Rationals

โœ Scribed by Carstenelsner

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
421 KB
Volume
189
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Let be a real irrational number, and a 2 0, b 2 0 , a > 1 be integers. A theorem of S. UCHIYAMA states that there are infinitely many pairs of integers u and v # 0 such that provided that it is not a z b z 0 mod s. It is shown that this result is best-possible for all integers s > 1.

1991 Mathematics Subject Classification. Primary 11 504; Secondary 11 J70.

๐Ÿ“œ SIMILAR VOLUMES

On the Convergence of Polynomial Approxi
On the Convergence of Polynomial Approximation of Rational Functions
โœ Guo-Jin Wang; Thomas W. Sederberg; Falai Chen ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 389 KB

This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r\_r