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A101314
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Decimal expansion of constant K, the unique solution > 1 to 2*Pi*log(k) == Pi*(1 - 1/k).
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1
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2, 8, 4, 6, 6, 8, 1, 3, 7, 0, 4, 0, 8, 3, 8, 4, 6, 1, 6, 8, 0, 2, 2, 5, 6, 7, 6, 7, 6, 9, 7, 1, 9, 1, 3, 0, 9, 8, 6, 5, 0, 2, 6, 7, 0, 5, 8, 5, 0, 4, 5, 4, 3, 1, 5, 1, 6, 9, 3, 1, 4, 7, 0, 9, 7, 7, 6, 6, 8, 9, 4, 3, 9, 0, 2, 5, 9, 2, 4, 4, 3, 7, 8, 3, 9, 6, 3, 7, 5, 5, 9, 8, 6, 0, 1, 1, 0, 7, 5, 0, 6, 3, 7, 4, 3
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OFFSET
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0,1
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COMMENTS
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Decimal expansion of the number K > 1 such that the surface area equals the volume of Gabriel's horn from x=1 to x=K, where x is the radial (central) axis and Gabriel's horn is a function y=1/x rotated about the x-axis.
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LINKS
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FORMULA
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-1/(2*ProductLog(-1, -1/(2*sqrt(e))))
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EXAMPLE
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0.2846681370408384616802256767697191309865026705850454315169314709776689439...
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MATHEMATICA
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RealDigits[ -1/(2*ProductLog[ -1, -1/(2*Sqrt[E])]), 10, 128][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 23 2004
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STATUS
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approved
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