%I A132116
%S A132116 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,
%T A132116 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,
%U A132116 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
%N A132116 Continued fraction expansion of pi/sqrt(3) = sqrt{2*zeta(2)}.
%C A132116 The decimal expansion is A093602.
%C A132116 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 generalised 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."
%H A132116 Jean Dolbeault, Ari Laptev and Michael Loss, <a href="http://arXiv.org/
               pdf/0708.1165">Lieb-Thirring inequalities with improved constants</
               a>
%e A132116 1 + 1/1 + 1/4 + 1/2 + 1/1 + 1/2 + 1/3 + 1/7 + 1/3 + 1/3 + 1/30 + 1/2 
               + 1/1 + 1/2 + 1/2 + 1/83 + 1/9 + 1/20 + 1/1 + 1/37 + 1/1 + 1/2 + 
               1/7 + 1/1 + 1/1 + 1/2 + 1/1 + 1/6 + 1/1 + 1/2 + 1/1 + 1/1 + 1/3 + 
               1/3 + 1/1 + 1/4 + 1/8 + 1/1 + 1/6 + 1/33 + 1/1 + 1/1 + 1/1 + 1/17 
               + 1/4 + 1/1 + 1/3 + 1/1 + 1/5 + 1/3 + 1/2 + 1/1 + 1/1100 + 1/2 + 
               1/31 + 1/6 + 1/7 + 1/1 + 1/1 + 1/9 + 1/6 + 1/3 + 1/1 + 1/2 + 1/2 
               + 1/2 + 1/1 + 1/2 + 1/4 + 1/6 + 1/16 + 1/1 + 1/1 + 1/8 + 1/1 + 1/
               13 + 1/2 + 1/18 + 1/1 + 1/4 + 1/1 + 1/46 + 1/2 + 1/5 + 1/1 + 1/3 
               + 1/1 + 1/42 + 1/1 + 1/1 + 1/1 + 1/26 + 1/3 + 1/2 + 1/1 + 1/5 + 1/
               4 + 1/4 + 1/5 + 1/1 + . . .
%Y A132116 Cf. A093602.
%Y A132116 Sequence in context: A046096 A080816 A016507 this_sequence A097525 A010124 
               A071406
%Y A132116 Adjacent sequences: A132113 A132114 A132115 this_sequence A132117 A132118 
               A132119
%K A132116 cofr,easy,nonn
%O A132116 1,3
%A A132116 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 10 2007