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A367899 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(k/n^2).

%I A367899 #10 Feb 16 2025 08:34:06
%S A367899 8,2,6,7,9,8,4,6,4,3,9,4,9,7,1,3,7,1,8,3,5,3,6,4,6,4,9,4,4,6,4,3,0,0,
%T A367899 6,3,7,8,3,3,9,9,7,8,2,3,6,7,0,2,9,1,2,0,2,4,1,0,6,0,1,8,1,8,8,0,5,8,
%U A367899 0,9,8,7,7,2,5,7,2,6,3,3,2,3,3,7,2,6,7,7,2,7,2,5,5,6,9,2,3,8,0,7,4,1,3,1,8,6
%N A367899 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(k/n^2).
%H A367899 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A367899 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A367899 Equals exp(1/24 + 3*zeta(3)/(8*Pi^2)) / (sqrt(A) * (2*Pi)^(1/12)), where A = A074962 is the Glaisher-Kinkelin constant.
%F A367899 Equals exp(Integral_{x=0..1} x*log(BarnesG(x)) dx).
%e A367899 0.82679846439497137183536464944643006378339978236702912024106018188...
%t A367899 RealDigits[E^(1/24 + 3*Zeta[3]/(8*Pi^2))/(Sqrt[Glaisher]*(2*Pi)^(1/12)), 10, 120][[1]]
%t A367899 Exp[Integrate[x*Log[BarnesG[x]], {x, 0, 1}]]
%Y A367899 Cf. A074962, A367842, A367898.
%K A367899 nonn,cons
%O A367899 0,1
%A A367899 _Vaclav Kotesovec_, Dec 04 2023