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

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

Table of n, a(n) for n=0..104.

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

Cf. A074962, A087013, A087014, A087015, A087016, A087017, A252798, A252799, A252851.

Sequence in context: A077106 A255287 A257342 * A316163 A346908 A195717

Adjacent sequences: A252847 A252848 A252849 * A252851 A252852 A252853

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Dec 23 2014

Status

approved