OFFSET
0,2
LINKS
Victor S. Adamchik, Contributions to the Theory of the Barnes function, arXiv:math/0308086 [math.CA], 2003.
Junesang Choi, H. M. Srivastava, and Victor S. Adamchik, Multiple Gamma and Related Functions, Applied Mathematics and Computation, Volume 134, Issues 2-3, 25 January 2003, pp. 515-533, see p. 7.
Eric Weisstein's MathWorld, Barnes G-Function.
Wikipedia, Barnes G-function.
FORMULA
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).
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
EXAMPLE
0.1889099312079046707636104110876410524175283515393316861419...
MATHEMATICA
RealDigits[BarnesG[1/6], 10, 105] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Dec 23 2014
STATUS
approved