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A132116
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Continued fraction expansion of Pi/sqrt(3).
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2
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1, 1, 4, 2, 1, 2, 3, 7, 3, 3, 30, 2, 1, 2, 2, 83, 9, 20, 1, 37, 1, 2, 7, 1, 1, 2, 1, 6, 1, 2, 1, 1, 3, 3, 1, 4, 8, 1, 6, 33, 1, 1, 1, 17, 4, 1, 3, 1, 5, 3, 2, 1, 1100, 2, 31, 6, 7, 1, 1, 9, 6, 3, 1, 2, 2, 2, 1, 2, 4, 6, 16, 1, 1, 8, 1, 13, 2, 18, 1, 4, 1, 46, 2, 5, 1, 3, 1, 42, 1, 1, 1, 26, 3, 2, 1, 5, 4
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OFFSET
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0,3
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COMMENTS
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Dolbeault et al. Abstract, where this is referred to as "the semiclassical constant" following remark 2, p. 2: "Following Eden and Foias we obtain a matrix version of a generalized Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schroedinger operators."
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LINKS
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MAPLE
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with(numtheory): cfrac(Pi/(sqrt(3)), 100, 'quotients'); # Muniru A Asiru, Sep 28 2018
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MATHEMATICA
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ContinuedFraction[Pi/Sqrt[3], 100] (* G. C. Greubel, Sep 27 2018 *)
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PROG
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(PARI) default(realprecision, 100); contfrac(Pi/sqrt(3)) \\ G. C. Greubel, Sep 27 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(Pi(R)/Sqrt(3)); // G. C. Greubel, Sep 27 2018
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CROSSREFS
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KEYWORD
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cofr,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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