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A252799
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Decimal expansion of G(2/3) where G is the Barnes G-function.
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8
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7, 7, 6, 8, 4, 9, 3, 8, 5, 7, 7, 6, 1, 8, 1, 4, 7, 7, 3, 0, 1, 1, 8, 3, 4, 3, 9, 2, 2, 1, 5, 4, 9, 9, 8, 0, 8, 0, 4, 0, 4, 7, 1, 3, 6, 3, 4, 5, 3, 8, 1, 3, 0, 0, 6, 2, 4, 5, 8, 7, 5, 2, 3, 8, 8, 7, 3, 0, 1, 2, 8, 1, 2, 8, 5, 0, 0, 0, 6, 0, 4, 0, 0, 9, 7, 4, 7, 4, 3, 0, 3, 1, 4, 8, 2, 4, 3, 7, 0, 5, 7, 9, 6, 1, 6
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OFFSET
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0,1
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LINKS
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FORMULA
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(3^(1/72)*e^(1/9 + (-2*Pi^2 + 3*PolyGamma(1, 1/3))/(36*sqrt(3)*Pi)))/(A^(4/3)*Gamma(2/3)^(1/3)), 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
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EXAMPLE
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0.7768493857761814773011834392215499808040471363453813...
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MATHEMATICA
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RealDigits[BarnesG[2/3], 10, 105] // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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