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%I #21 Jan 17 2020 05:30:02
%S 2,2,3,5,8,8,5,5,9,5,5,0,8,9,6,9,8,6,4,2,8,3,9,6,4,7,9,9,3,1,1,8,9,0,
%T 6,4,4,8,4,5,1,5,9,1,2,2,8,5,9,5,2,4,7,4,7,7,9,3,4,4,7,9,7,8,2,6,0,6,
%U 2,7,0,8,1,4,5,7,2,5,2,2,1,7,9,3,2,8,3,2,0,2,9,5,2,8,3,2,3,4,6,2,8,9,8,2
%N Decimal expansion of D(1), where D(x) is the infinite product function defined in the formula section (or in the Finch reference).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 136.
%H G. C. Greubel, <a href="/A241421/b241421.txt">Table of n, a(n) for n = 1..5000</a>
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 20.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>
%F D(x) = lim_{n->infinity} ( Prod_{k=1..2n+1} (1+x/k)^((-1)^(k+1)*k) ).
%F D(x) = (e^(x/2-1/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x-2)*Gamma((x+1)/2)^(1-x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the Glaisher-Kinkelin constant and G is the Barnes G-function.
%F D(1) = A^6/(2^(1/6)*sqrt(Pi)).
%e 2.23588559550896986428396479931189064484515912285952474779344797826...
%t RealDigits[Glaisher^6/(2^(1/6)*Sqrt[Pi]), 10, 104] // First
%o (PARI) default(realprecision, 100); A=exp(1/12-zeta'(-1)); A^6/(2^(1/6)* sqrt(Pi)) \\ _G. C. Greubel_, Aug 24 2018
%Y Cf. A006752, A019610 (D(2)), A074962, A241420 (D(1/2)).
%K nonn,cons,easy
%O 1,1
%A _Jean-François Alcover_, Aug 08 2014
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