APPROXIMATION BY Ω− CONTINUED FRACTIONS
https://doi.org/10.22405/2226-8383-2013-14-4-95-100
Abstract
Let x ∈ (0, 1) be a real number, x = [0; ε1/b1, . . . , ε1/bn, . . .] be its expansion in Ω− continued fraction. Let An/Bn be its nth convergent and Υn = Υn(x) = B2 n |x − An/Bn|. In this note we prove the analog of the classical theorems by Borel and Hurwitz on the quality of the approximations for Ω− continued fractions: min(Υn−1, Υn, Υn+1) 6 1/ √ 5. The result is best possible.
About the Author
O. A. Gorkusha
Хабаровское отделение Института прикладной математики Дальневосточного отделения Российской академии наук
Russian Federation
Russian Federation
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Review
For citations:
Gorkusha O.A. APPROXIMATION BY Ω− CONTINUED FRACTIONS. Chebyshevskii Sbornik. 2013;14(4):95-100. (In Russ.) https://doi.org/10.22405/2226-8383-2013-14-4-95-100
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