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Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).
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%I #29 Sep 23 2022 16:37:56

%S 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,

%T 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,

%U 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

%N Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).

%C Also known as the 4th Bendersky constant.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.

%H G. C. Greubel, <a href="/A243264/b243264.txt">Table of n, a(n) for n = 0..2002</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.

%F 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.

%F A(4) = exp(-zeta'(-4)) = exp(-3*zeta(5)/(4*Pi^4)).

%F A(4) = exp((B(4)/4)*(zeta(5)/zeta(4))). - _G. C. Greubel_, Dec 31 2015

%e 0.9920479745250402600134369776254433567369...

%t RealDigits[Exp[-3*Zeta[5]/(4*Pi^4)], 10, 98] // First

%t RealDigits[Exp[N[(BernoulliB[4]/4)*(Zeta[5]/Zeta[4]), 100]]] // First (* _G. C. Greubel_, Dec 31 2015 *)

%Y Cf. A255323, A259069.

%Y Cf. A019727, A074962, A243262, A243263, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jun 02 2014