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A243264 Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).

%I A243264 #33 Feb 16 2025 08:33:22
%S A243264 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 A243264 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 A243264 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 A243264 Decimal expansion of the generalized Glaisher-Kinkelin constant A(4).
%C A243264 Also known as the 4th Bendersky constant.
%D A243264 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.
%H A243264 G. C. Greubel, <a href="/A243264/b243264.txt">Table of n, a(n) for n = 0..2002</a>
%H A243264 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A243264 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 A243264 A(4) = exp(-zeta'(-4)) = exp(-3*zeta(5)/(4*Pi^4)).
%F A243264 A(4) = exp((B(4)/4)*(zeta(5)/zeta(4))). - _G. C. Greubel_, Dec 31 2015
%e A243264 0.9920479745250402600134369776254433567369...
%t A243264 RealDigits[Exp[-3*Zeta[5]/(4*Pi^4)], 10, 98] // First
%t A243264 RealDigits[Exp[N[(BernoulliB[4]/4)*(Zeta[5]/Zeta[4]), 100]]] // First (* _G. C. Greubel_, Dec 31 2015 *)
%o A243264 (PARI) exp(-3*zeta(5)/(4*Pi^4)) \\ _Stefano Spezia_, Dec 01 2024
%Y A243264 Cf. A255323, A259069.
%Y A243264 Cf. A019727, A074962, A243262, A243263, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.
%K A243264 nonn,cons
%O A243264 0,1
%A A243264 _Jean-François Alcover_, Jun 02 2014