OFFSET
0,3
COMMENTS
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."
The inverse, sqrt(3)/Pi, which has the same continued fraction expansion (up to an initial zero), appears in geometric considerations involving spheres, see for example A343235. - M. F. Hasler, Oct 29 2024
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..9999
Jean Dolbeault, Ari Laptev and Michael Loss, Lieb-Thirring inequalities with improved constants, arXiv:0708.1165 [math.AP], 2007.
MAPLE
with(numtheory): cfrac(Pi/(sqrt(3)), 100, 'quotients'); # Muniru A Asiru, Sep 28 2018
MATHEMATICA
ContinuedFraction[Pi/Sqrt[3], 100] (* G. C. Greubel, Sep 27 2018 *)
PROG
(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
CROSSREFS
KEYWORD
cofr,easy,nonn
AUTHOR
Jonathan Vos Post, Aug 10 2007
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 09 2024
STATUS
approved