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

0,1

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.

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.

Example

-0.242095898582598841775723030153544722318916336881701342613272218...

Mathematica

RealDigits[(1/6) Pi^2 (1 + Log[2Pi] - 12 Log[Glaisher]), 10, 101][[1]]

Prog

(PARI) default(realprecision, 100); (1/6)*(1-Euler)*Pi^2 + zeta'(2) \\ G. C. Greubel, Sep 07 2018

Crossrefs

Cf. A001620, A073002, A074962.

Sequence in context: A364529 A300329 A094239 * A201316 A105023 A279315

Adjacent sequences: A273237 A273238 A273239 * A273241 A273242 A273243

Keyword

nonn,cons,easy

Author

Jean-François Alcover, May 18 2016

Status

approved