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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 92–109 (Mi izv1633)  

This article is cited in 4 scientific papers (total in 4 papers)

On the approximation of $x^\alpha$ by rational functions

N. S. Vyacheslavov


Abstract: Weak equivalence type estimates are obtained for the smallest deviation of $x^\alpha$ ($\alpha$ a proper fraction) from the rational functions of degree not greater than $n=1,2,…$ in the metrics of $L_p[0,1]$ ($1\leqslant p\leqslant\infty$).
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 83–101

Bibliographic databases:

UDC: 517.5
MSC: 41A20
Received: 18.12.1978

Citation: N. S. Vyacheslavov, “On the approximation of $x^\alpha$ by rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 92–109; Math. USSR-Izv., 16:1 (1981), 83–101

Citation in format AMSBIB
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\by N.~S.~Vyacheslavov
\paper On the approximation of $x^\alpha$ by rational functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 92--109
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=563787}
\zmath{https://zbmath.org/?q=an:0465.41001|0426.41010}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 83--101
\crossref{https://doi.org/10.1070/IM1981v016n01ABEH001297}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LP24600005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Richard S. Varga, Amos J. Carpenter, “Some numerical results on best uniform rational approximation ofx α on [0,1]”, Numer Algor, 2:2 (1992), 171  crossref  mathscinet  zmath
    2. H. Stahl, “Best uniform rational approximation of $|x|$ on $[-1,1]$”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 461–487  mathnet  crossref  mathscinet  zmath  isi
    3. Amos J. Carpenter, “Scientific computation on some mathematical problems”, Journal of Computational and Applied Mathematics, 66:1-2 (1996), 111  crossref
    4. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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