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A225746
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Decimal expansion of the logarithm of Glaisher's constant.
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3
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0, 2, 4, 8, 7, 5, 4, 4, 7, 7, 0, 3, 3, 7, 8, 4, 2, 6, 2, 5, 4, 7, 2, 5, 2, 9, 9, 3, 5, 7, 6, 1, 1, 3, 9, 7, 6, 0, 9, 7, 3, 6, 9, 7, 1, 3, 6, 6, 8, 5, 3, 5, 1, 1, 6, 9, 9, 9, 8, 5, 5, 6, 3, 9, 6, 9, 0, 6, 9, 3, 0, 3, 2, 9, 9, 9, 9, 1, 0, 5, 0, 6, 0, 9, 2, 8, 5, 8, 4, 3, 3, 6, 6, 5, 8, 4, 2, 0, 8, 8, 8
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.
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LINKS
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FORMULA
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Equals 1/12 - zeta'(-1).
Also equals (gamma + log(2*Pi))/12 -zeta'(2)/(2*Pi^2).
Equals lim_{n->oo} (Sum_{k=1..n} k*log(k) - (n^2/2 + n/2 + 1/12)*log(n) + n^2/4).
Equals 1/8 + (1/2) * Sum_{n>=0} ((1/(n+1)) * Sum_{k=0..n} (-1)^(k+1) * binomial(n,k) * (k+1)^2 * log(k+1)) (Guillera and Sondow, 2008). (End)
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EXAMPLE
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0.248754477033784262547252993576113976097369713668535116999855639690693032999...
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MATHEMATICA
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RealDigits[Log[Glaisher], 10, 100] // First
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PROG
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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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