A348731 - OEIS

%I #13 Oct 31 2021 10:22:40

%S 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,

%T 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,

%U 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

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

%F Equals Pi^2/54 - PolyGamma(1, 2/3)/9. - _Vaclav Kotesovec_, Oct 31 2021

%e -0.15766014916783233039054467406996221822374946546295676913413604497322566...

%t RealDigits[Integrate[x*Log[x]/(1 + x + x^2), {x, 0, 1}], 10, 100][[1]] (* _Amiram Eldar_, Oct 31 2021 *)

%t RealDigits[Pi^2/54 - PolyGamma[1, 2/3]/9, 10, 100][[1]] (* _Vaclav Kotesovec_, Oct 31 2021 *)

%o (SageMath)

%o RealField(25)(numerical_integral(x*log(x)/(1+x+x^2), 0, 1)[0])

%o (PARI) intnum(x=0, 1, x*log(x)/(1+x+x^2)) \\ _Michel Marcus_, Oct 31 2021

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

%K nonn,cons

%O 0,2

%A _Dumitru Damian_, Oct 31 2021