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A367898 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(1/n).

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%I A367898 #10 Feb 16 2025 08:34:06
%S A367898 4,1,7,4,2,7,2,9,7,6,0,1,4,0,9,8,6,3,6,4,3,9,4,8,4,5,1,6,2,2,5,1,6,9,
%T A367898 7,7,0,9,4,5,9,6,3,3,2,2,1,4,1,1,0,0,8,2,3,2,1,1,3,1,7,6,8,2,0,0,0,9,
%U A367898 5,8,8,8,9,2,9,8,5,6,6,3,7,9,1,9,4,6,9,5,0,3,6,9,4,0,2,4,5,7,1,4,8,2,8,0,7,6
%N A367898 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(1/n).
%H A367898 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A367898 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A367898 Equals exp(1/12) / (A^2 * (2*Pi)^(1/4)), where A = A074962 is the Glaisher-Kinkelin constant.
%F A367898 Product_{k=1..n} BarnesG(k/n) = A^(1/n - n) * exp((n - 1/n)/12) * n^(1/2 + 1/(12*n)) * (2*Pi)^((1-n)/2) * Product_{k=1..n-1} Gamma(k/n)^(k/n).
%e A367898 0.4174272976014098636439484516225169770945963322141100823211317682...
%t A367898 RealDigits[Exp[1/12] / (Glaisher^2 * (2*Pi)^(1/4)), 10, 120][[1]]
%Y A367898 Cf. A074962, A367842, A367899.
%K A367898 nonn,cons
%O A367898 0,1
%A A367898 _Vaclav Kotesovec_, Dec 04 2023