%I #15 Jun 11 2024 02:07:11

%S 9,0,9,7,9,9,1,9,5,8,8,8,5,9,4,0,0,6,0,6,1,4,8,8,4,0,7,2,4,5,5,8,4,9,

%T 6,9,2,9,7,7,4,4,9,4,6,9,8,7,7,5,4,7,1,2,1,8,0,7,1,9,4,0,9,1,4,7,6,9,

%U 6,9,1,0,7,0,9,1,3,5,7,1,7,4,7,0,6,8,1,7,4,6,0,2,1,8,6,6,5,3,9

%N Decimal expansion of G(5/6) where G is the Barnes G-function.

%H 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 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, Pages 515-533, see p. 7.

%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 Equals e^(5/72 - Pi/(12*sqrt(3)) + PolyGamma(1, 1/3)/(8*sqrt(3)*Pi))/(2^(1/72)*3^(1/144)*A^(5/6)*Gamma(5/6)^(1/6)), where PolyGamma(1, .) is the derivative of the digamma function and A the Glaisher-Kinkelin constant (A074962).

%F 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 0.90979919588859400606148840724558496929774494698775471218...

%t RealDigits[BarnesG[5/6], 10, 99] // First

%Y Cf. A074962, A087013, A087014, A087015, A087016, A087017, A252798, A252799, A252850.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Dec 23 2014