A262605 Decimal expansion of Integral_{0..1} log(1-x)*log(x)^2 dx (negated).

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

Offset

0,1

Links

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

M. Jung, Y. J. Cho, J. Choi, Euler sums evaluatable from integrals, Commun. Korean Math. Soc. 19 (2008), 545-555.

Formula

Equals -6 + Pi^2/3 + 2 zeta(3).

Equals Integral_{0..Pi/2} log(cos(x)^2) * log(sin(x)^2)^2 * sin(2x) dx.

Example

-0.30601805998435855625569334368504964003212761290540536094434 ...

Mathematica

RealDigits[Integrate[Log[1 - x]*Log[x]^2, {x, 0, 1}] , 10,
  105] // First

Prog

(PARI) -(-6 + Pi^2/3 + 2*zeta(3)) \\ Michel Marcus, Sep 27 2015

Crossrefs

Cf. A152416 (Integral_{0..1} log(1-x)*log(x) dx), A262606 (Integral_{0..1} log(1-x)^2*log(x)^2 dx).

Sequence in context: A060147 A268142 A321254 * A092731 A348080 A201567

Adjacent sequences: A262602 A262603 A262604 * A262606 A262607 A262608

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 26 2015

Status

approved