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A074962
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Decimal expansion of Glaisher-Kinkelin constant A.
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9
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1, 2, 8, 2, 4, 2, 7, 1, 2, 9, 1, 0, 0, 6, 2, 2, 6, 3, 6, 8, 7, 5, 3, 4, 2, 5, 6, 8, 8, 6, 9, 7, 9, 1, 7, 2, 7, 7, 6, 7, 6, 8, 8, 9, 2, 7, 3, 2, 5, 0, 0, 1, 1, 9, 2, 0, 6, 3, 7, 4, 0, 0, 2, 1, 7, 4, 0, 4, 0, 6, 3, 0, 8, 8, 5, 8, 8, 2, 6, 4, 6, 1, 1, 2, 9, 7, 3, 6, 4, 9, 1, 9, 5, 8, 2, 0, 2, 3, 7, 4, 3, 9, 4, 2, 0, 6, 4, 6, 1, 2, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Arise in various asymptotic expressions such as A002109(n)=1^1*2^2*3^3*...*n^n which is asymptotic to A*n^(n^2/2+n/2+1/12)*exp(-n^2/4). See A002109 for more references and links.
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REFERENCES
| S. R. Finch, Mathematical constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 135.
O. Furdui, proposer, Problem 11494, Amer. Math. Monthly, 118 (2011), 850-852.
K. Knopp, "Theory and applications of infinite series", Dover, p. 555.
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LINKS
| Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant
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FORMULA
| A=1.2824271291... A = 2^(1/36)*Pi^(1/6)*exp(1/3*(-Gamma/4+s(2)/3-s(3)/4+...)) where s(k) denotes sum(n>=0, 1/(2n+1)^k) . Closed expressions for A are exp(-zeta'(2)/2/Pi^2 + log(2*Pi)/12 + Gamma/12) or exp(1/12-zeta'(-1))
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MATHEMATICA
| RealDigits[ Glaisher, 10, 111][[1]] (* RGWv *)
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PROG
| (PARI) x=10^(-100); exp(1/12-(zeta(-1+x)-zeta(-1))/x)
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CROSSREFS
| Sequence in context: A173686 A090975 A199715 * A064863 A021358 A203022
Adjacent sequences: A074959 A074960 A074961 * A074963 A074964 A074965
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KEYWORD
| cons,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 05 2002
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Feb 03 2003
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