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Search: id:A126774
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| A126774 |
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Decimal expansion of volume of conjectured unique minimal closed orientable 3-manifold. |
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+0
1
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| 9, 4, 2, 7, 0, 7, 3, 6, 2, 7, 7, 6, 9, 2, 7, 7, 2, 0, 9, 2, 1, 2, 9, 9, 6, 0, 3, 0, 9, 2, 2, 1, 1, 6, 4, 7, 5, 9, 0, 3, 2, 7, 1, 0, 5, 7, 6, 6, 8, 8, 3, 1, 5, 9, 0, 1, 4, 5, 0, 6, 7, 7, 5, 7, 5, 2, 9, 3, 4, 1, 8, 2, 7, 7, 4, 1, 5, 7, 2, 1, 0, 3, 1, 2, 3, 1, 5, 6, 7, 2, 6, 4, 3, 3, 3, 3, 0, 3, 5, 8, 0, 4, 1, 8, 0
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Conjectured, as of 2004. Bound cited for this hyperbolic space constant depends on Perelman's proof of Poincare conjecture, which proof is now believed to be true. Can S. R. Finch comment on the conjectured constant as of 2007?
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LINKS
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S. R. Finch, Volumes of hyperbolic 3-manifolds, PDF linked to from "Mathematical Constants", 9/5/2004.
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FORMULA
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Formula: Im(dilog(z0)+ln(|z0|)*ln(1-z0)) where z0 = 0.8774.. + 0.7448..i is the root of z^3-z^2+1 with Im(z)>0. - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
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EXAMPLE
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0.9427073627769277209212996030922116475903...
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PROGRAM
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(PARI) z0=polroots(z^3-z^2+1)[3]; imag(dilog(z0)+log(abs(z0))*log(1-z0)) - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
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CROSSREFS
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Sequence in context: A039663 A155535 A099879 this_sequence A050016 A033329 A097326
Adjacent sequences: A126771 A126772 A126773 this_sequence A126775 A126776 A126777
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KEYWORD
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cons,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 13 2007
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
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