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A252850 Decimal expansion of G(1/6) where G is the Barnes G-function.

%I A252850 #18 Feb 16 2025 08:33:24
%S A252850 1,8,8,9,0,9,9,3,1,2,0,7,9,0,4,6,7,0,7,6,3,6,1,0,4,1,1,0,8,7,6,4,1,0,
%T A252850 5,2,4,1,7,5,2,8,3,5,1,5,3,9,3,3,1,6,8,6,1,4,1,9,0,3,7,9,1,2,5,7,5,5,
%U A252850 7,8,1,4,2,6,8,8,8,2,7,9,3,4,6,4,9,9,6,8,0,4,8,6,1,6,5,9,5,5,5,4,2,9,0,4,7
%N A252850 Decimal expansion of G(1/6) where G is the Barnes G-function.
%H A252850 Victor 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 A252850 Junesang Choi, H. M. Srivastava, and Victor S. Adamchik, <a href="http://dx.doi.org/10.1016/S0096-3003(01)00301-0">Multiple Gamma and Related Functions</a>, Applied Mathematics and Computation, Volume 134, Issues 2-3, 25 January 2003, pp. 515-533, see p. 7.
%H A252850 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A252850 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A252850 Equals e^(5/72 + Pi/(12*sqrt(3)) - PolyGamma(1, 1/3)/(8*sqrt(3)*Pi))/(2^(1/72)*3^(1/144)*(A*Gamma(1/6))^(5/6)), where PolyGamma(1, .) is the derivative of the digamma function and A the Glaisher-Kinkelin constant (A074962).
%F A252850 G(1/6) * G(5/6) = A252850 * A252851 = exp(5/36) / (A^(5/3) * 2^(7/36) * 3^(1/72) * Pi^(1/6) * Gamma(1/6)^(2/3)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Mar 01 2015
%e A252850 0.1889099312079046707636104110876410524175283515393316861419...
%t A252850 RealDigits[BarnesG[1/6], 10, 105] // First
%Y A252850 Cf. A074962, A087013, A087014, A087015, A087016, A087017, A252798, A252799, A252851.
%K A252850 nonn,cons,easy
%O A252850 0,2
%A A252850 _Jean-François Alcover_, Dec 23 2014