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A243264
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Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).
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28
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9, 9, 2, 0, 4, 7, 9, 7, 4, 5, 2, 5, 0, 4, 0, 2, 6, 0, 0, 1, 3, 4, 3, 6, 9, 7, 7, 6, 2, 5, 4, 4, 3, 3, 5, 6, 7, 3, 6, 9, 0, 4, 8, 5, 1, 2, 7, 6, 1, 8, 8, 0, 8, 9, 3, 5, 2, 0, 9, 4, 6, 1, 4, 9, 1, 5, 5, 4, 1, 4, 5, 3, 8, 5, 3, 8, 9, 4, 5, 9, 7, 6, 1, 8, 0, 5, 7, 7, 3, 6, 1, 7, 2, 9, 5, 6, 4, 3
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OFFSET
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0,1
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COMMENTS
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Also known as the 4th 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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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(4) = exp(-zeta'(-4)) = exp(-3*zeta(5)/(4*Pi^4)).
A(4) = exp((B(4)/4)*(zeta(5)/zeta(4))). - G. C. Greubel, Dec 31 2015
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EXAMPLE
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0.9920479745250402600134369776254433567369...
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MATHEMATICA
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RealDigits[Exp[-3*Zeta[5]/(4*Pi^4)], 10, 98] // First
RealDigits[Exp[N[(BernoulliB[4]/4)*(Zeta[5]/Zeta[4]), 100]]] // First (* G. C. Greubel, Dec 31 2015 *)
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CROSSREFS
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Cf. A019727, A074962, A243262, A243263, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.
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KEYWORD
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AUTHOR
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STATUS
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approved
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