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A132116
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Continued fraction expansion of pi/sqrt(3) = sqrt{2*zeta(2)}.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The decimal expansion is A093602.
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."
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LINKS
| Jean Dolbeault, Ari Laptev and Michael Loss, Lieb-Thirring inequalities with improved constants
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EXAMPLE
| 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 + . . .
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CROSSREFS
| Cf. A093602.
Sequence in context: A046096 A080816 A016507 * A175665 A200586 A097525
Adjacent sequences: A132113 A132114 A132115 * A132117 A132118 A132119
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KEYWORD
| cofr,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 10 2007
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