A252851 Decimal expansion of G(5/6) where G is the Barnes G-function.

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..98.

Victor S. Adamchik, Contributions to the Theory of the Barnes function, arXiv:math/0308086 [math.CA], 2003.

Junesang Choi, H. M. Srivastava, Victor S. Adamchik, Multiple Gamma and Related Functions, Applied Mathematics and Computation, Volume 134, Issues 2-3, 25 January 2003, Pages 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^(5/6)*Gamma(5/6)^(1/6)), 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

0.90979919588859400606148840724558496929774494698775471218...

Mathematica

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

Crossrefs

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

Sequence in context: A154994 A237193 A132268 * A241290 A201298 A029687

Adjacent sequences: A252848 A252849 A252850 * A252852 A252853 A252854

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Dec 23 2014

Status

approved