cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Dumitru Damian, Oct 31 2021

Keywords

Examples

			-0.15766014916783233039054467406996221822374946546295676913413604497322566...
		

Crossrefs

Programs

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

Formula

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