A273240 Decimal expansion of Integral_{0..inf} x log(x)/(exp(x)-1) dx (negated).
2, 4, 2, 0, 9, 5, 8, 9, 8, 5, 8, 2, 5, 9, 8, 8, 4, 1, 7, 7, 5, 7, 2, 3, 0, 3, 0, 1, 5, 3, 5, 4, 4, 7, 2, 2, 3, 1, 8, 9, 1, 6, 3, 3, 6, 8, 8, 1, 7, 0, 1, 3, 4, 2, 6, 1, 3, 2, 7, 2, 2, 1, 8, 0, 1, 7, 0, 8, 1, 6, 2, 0, 1, 5, 7, 7, 1, 3, 3, 3, 1, 4, 9, 1, 0, 4, 3, 4, 8, 9, 9, 2, 9, 8, 1, 0, 2, 9, 7, 5, 9
Offset: 0
Examples
-0.242095898582598841775723030153544722318916336881701342613272218...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Donal F. Connon, Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(b), arXiv:0710.4024 [math.HO] 2007. page 130.
Programs
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Mathematica
RealDigits[(1/6) Pi^2 (1 + Log[2Pi] - 12 Log[Glaisher]), 10, 101][[1]]
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PARI
default(realprecision, 100); (1/6)*(1-Euler)*Pi^2 + zeta'(2) \\ G. C. Greubel, Sep 07 2018
Formula
Equals (1/6)*(1-EulerGamma)*Pi^2+zeta'(2).
Also equals (1/6)*Pi^2*(1+log(2*Pi)-12*log(G)), where G is the Glaisher-Kinkelin constant.