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A252850
Decimal expansion of G(1/6) where G is the Barnes G-function.
2
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, 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, 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
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved