A252798 Decimal expansion of G(1/3) where G is the Barnes G-function.

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

Offset

0,1

Links

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

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

Eric Weisstein's World of Mathematics, Barnes G-Function.

Wikipedia, Barnes G-function.

Formula

(3^(1/72)*e^(1/9 + (2*Pi^2 - 3*PolyGamma(1, 1/3))/(36*sqrt(3)*Pi)))/(A^(4/3)*Gamma(1/3)^(2/3)), where PolyGamma(1, .) is the derivative of the digamma function and A the Glaisher-Kinkelin constant (A074962).

G(1/3) * G(2/3) = A252798 * A252799 = 3^(7/36) * exp(2/9) / (A^(8/3) * 2^(1/3) * Pi^(1/3) * Gamma(1/3)^(1/3)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 01 2015

Example

0.4000785230907682022850145152603045579230386308284...

Mathematica

RealDigits[BarnesG[1/3], 10, 105] // First

Crossrefs

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

Sequence in context: A243000 A285214 A285340 * A373736 A169766 A003194

Adjacent sequences: A252795 A252796 A252797 * A252799 A252800 A252801

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Dec 22 2014

Status

approved