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A243265
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Decimal expansion of the generalized Glaisher-Kinkelin constant A(5).
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27
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1, 0, 0, 9, 6, 8, 0, 3, 8, 7, 2, 8, 5, 8, 6, 6, 1, 6, 1, 1, 2, 0, 0, 8, 9, 1, 9, 0, 4, 6, 2, 6, 3, 0, 6, 9, 2, 6, 0, 3, 2, 7, 6, 3, 4, 7, 2, 1, 1, 5, 2, 4, 9, 1, 8, 4, 6, 0, 9, 2, 4, 7, 2, 1, 5, 6, 2, 3, 0, 1, 4, 2, 5, 0, 0, 3, 4, 1, 0, 0, 3, 2, 7, 7, 0, 1, 5, 0, 5, 6, 5, 9, 6, 5, 2, 7, 6, 4, 5, 5, 5, 9, 4
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OFFSET
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1,4
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COMMENTS
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Also known as the 5th Bendersky constant.
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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. 137.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..2004
Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant
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FORMULA
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A(k) = exp(B(k+1)/(k+1)*H(k)-zeta'(-k)), where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.
A(5) = exp(137/15120-zeta'(-5)).
Equals exp(gamma/252 - 15*Zeta'(6)/(4*Pi^6)) * (2*Pi)^(1/252), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015
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EXAMPLE
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1.00968038728586616112008919046263...
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MATHEMATICA
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RealDigits[Exp[137/15120-Zeta'[-5]], 10, 103] // First
RealDigits[Exp[N[(BernoulliB[6]/6)*(EulerGamma + Log[2*Pi] - Zeta'[6]/Zeta[6]), 200]]]//First (* G. C. Greubel, Dec 31 2015 *)
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CROSSREFS
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Cf. A255344, A259070.
Cf. A019727, A074962, A243262, A243263, A243264, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.
Sequence in context: A019643 A011012 A157989 * A248472 A306553 A011194
Adjacent sequences: A243262 A243263 A243264 * A243266 A243267 A243268
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KEYWORD
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nonn,cons
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AUTHOR
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Jean-François Alcover, Jun 02 2014
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STATUS
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approved
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