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A272354
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Decimal expansion of 'kappa', an asymptotic enumeration constant related to unit interval graphs.
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0
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6, 2, 3, 1, 1, 9, 8, 9, 6, 3, 9, 1, 9, 1, 1, 3, 8, 5, 2, 0, 4, 8, 6, 6, 0, 2, 9, 3, 2, 8, 2, 2, 2, 8, 5, 1, 6, 8, 1, 8, 1, 1, 1, 1, 5, 7, 6, 9, 1, 8, 2, 8, 5, 0, 9, 1, 4, 7, 5, 2, 3, 3, 3, 5, 1, 1, 2, 2, 7, 1, 6, 1, 2, 9, 9, 9, 8, 5, 8, 2, 9, 4, 3, 3, 0, 8, 7, 4, 5, 0, 7, 3, 1, 7, 5, 7, 4, 8, 7
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6.7 More Graph Varieties, p. 309.
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LINKS
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FORMULA
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kappa = exp(-sqrt(3)/4)*exp(-Sum_{j >= 2} (psi(4^(-j))/j, where psi(x)=(1 + 2*x - sqrt(1 - 4*x)*sqrt(1 - 4*x^2))/(4*sqrt(1 - 4*x^2)).
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EXAMPLE
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0.6231198963919113852048660293282228516818111157691828509147523335...
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MATHEMATICA
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digits = 99; psi[x_] := (1 + 2*x - Sqrt[1 - 4*x]*Sqrt[1 - 4*x^2])/(4*Sqrt[1 - 4*x^2]);
kappa = Exp[-Sqrt[3]/4]*Exp[-NSum[psi[4^(-j)]/j, {j, 2, Infinity}, NSumTerms -> 200, WorkingPrecision -> digits + 5]]; RealDigits[kappa, 10, digits][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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