A348731 Decimal expansion of Integral_{x=0..1} x*log(x)/(1+x+x^2) dx (negated).

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

Offset

0,2

Links

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

Formula

Equals Pi^2/54 - PolyGamma(1, 2/3)/9. - Vaclav Kotesovec, Oct 31 2021

Example

-0.15766014916783233039054467406996221822374946546295676913413604497322566...

Mathematica

RealDigits[Integrate[x*Log[x]/(1 + x + x^2), {x, 0, 1}], 10, 100][[1]] (* Amiram Eldar, Oct 31 2021 *)
RealDigits[Pi^2/54 - PolyGamma[1, 2/3]/9, 10, 100][[1]] (* Vaclav Kotesovec, Oct 31 2021 *)

Prog

(SageMath)
RealField(25)(numerical_integral(x*log(x)/(1+x+x^2), 0, 1)[0])
(PARI) intnum(x=0, 1, x*log(x)/(1+x+x^2)) \\ Michel Marcus, Oct 31 2021

Crossrefs

Cf. A072691, A086722, A086724, A111003, A222171.

Sequence in context: A318733 A195444 A114603 * A346590 A100554 A258148

Adjacent sequences: A348728 A348729 A348730 * A348732 A348733 A348734

Keyword

nonn,cons

Author

Dumitru Damian, Oct 31 2021

Status

approved