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%I #10 Mar 01 2015 07:15:03
%S 4,0,0,0,7,8,5,2,3,0,9,0,7,6,8,2,0,2,2,8,5,0,1,4,5,1,5,2,6,0,3,0,4,5,
%T 5,7,9,2,3,0,3,8,6,3,0,8,2,8,4,1,7,5,9,8,5,9,5,3,3,2,7,0,6,2,1,9,0,9,
%U 3,8,8,9,0,3,7,1,4,6,0,9,2,0,9,0,7,5,2,9,6,6,9,9,4,6,0,2,9,9,0,2,6,9,5,6,5
%N Decimal expansion of G(1/3) where G is the Barnes G-function.
%H V. S. Adamchik, <a href="http://arxiv.org/abs/math/0308086">Contributions to the Theory of the Barnes function</a>, arXiv:math/0308086 [math.CA], 2003.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F (3^(1/72)*e^(1/9 + (2*Pi^2 - 3*PolyGamma(1, 1/3))/(36*sqrt(3)*Pi)))/(A^(4/3)*Gamma(1/3)^(2/3)), where PolyGamma(1, .) is the derivative of the digamma function and A the Glaisher-Kinkelin constant (A074962).
%F G(1/3) * G(2/3) = A252798 * A252799 = 3^(7/36) * exp(2/9) / (A^(8/3) * 2^(1/3) * Pi^(1/3) * GAMMA(1/3)^(1/3)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Mar 01 2015
%e 0.4000785230907682022850145152603045579230386308284...
%t RealDigits[BarnesG[1/3], 10, 105] // First
%Y Cf. A074962, A087013, A087014, A087015, A087016, A087017, A252799.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Dec 22 2014
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