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
Examples
0.4000785230907682022850145152603045579230386308284...
Links
- 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.
Programs
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Mathematica
RealDigits[BarnesG[1/3], 10, 105] // First
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