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%I #46 Aug 14 2020 01:28:31
%S 1,0,3,0,9,1,6,7,5,2,1,9,7,3,9,2,1,1,4,1,9,3,3,1,3,0,9,6,4,6,6,9,4,2,
%T 2,9,0,6,3,3,1,9,4,3,0,6,4,0,3,4,8,7,0,6,0,2,2,7,2,6,1,7,4,1,1,4,5,1,
%U 6,6,0,6,6,9,7,8,2,9,0,4,0,5,2,9,2,9,3,1,3,6,2,5,5,4,8,0,8,8,5
%N Decimal expansion of the generalized Glaisher-Kinkelin constant A(2).
%C Also known as the second Bendersky constant.
%C This is likely the same as the constant B considered in section 3 of the Choi and Srivastava link. - _R. J. Mathar_, Oct 03 2016
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.
%H G. C. Greubel, <a href="/A243262/b243262.txt">Table of n, a(n) for n = 1..2002</a>
%H J. Choi and H. M. Srivastava, <a href="http://dx.doi.org/10.1006/jmaa.1998.6216">Certain classes of series involving the zeta function</a>, J. Math. Annal. Applic. 231 (1999) 91-117.
%H K. Kimoto, N. Kurokawa, C. Sonoki, M. Wakayama, <a href="http://www.math.u-ryukyu.ac.jp/~kimoto/pdf/kksw2.pdf">Some examples of generalized zeta regularized products</a>, Kodai Math. J. 27 (2004), 321-335.
%H Tobias Kyrion, <a href="https://arxiv.org/abs/2008.05573">A closed-form expression for zeta(3)</a>, arXiv:2008.05573 [math.GM], 2020.
%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(0) = sqrt(2*Pi) (A019727),
%F A(1) = A = Glaisher-Kinkelin constant (A074962),
%F A(2) = exp(-zeta'(-2)) = exp(zeta(3)/(4*Pi^2)).
%F Equals exp(-A240966). - _Vaclav Kotesovec_, Feb 22 2015
%e 1.03091675219739211419331309646694229...
%t RealDigits[Exp[Zeta[3]/(4*Pi^2)], 10, 99] // First
%t RealDigits[Exp[N[(BernoulliB[2]/4)*(Zeta[3]/Zeta[2]), 200]]]//First (* _G. C. Greubel_, Dec 31 2015 *)
%o (PARI) exp(zeta(3)/(4*Pi^2)) \\ _Felix Fröhlich_, Jun 27 2019
%Y Cf. A051675, A055462, A240966, A255269.
%Y Cf. A019727, A074962, A243263, A243264, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.
%Y Cf. A002117 (zeta(3)).
%K nonn,cons
%O 1,3
%A _Jean-François Alcover_, Jun 02 2014
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