A258750 Decimal expansion of Ls_4(Pi), the value of the 4th basic generalized log-sine integral at Pi.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.

Formula

-Integral_{0..Pi} log(2*sin(t/2))^3 dx = (3/2)*Pi*zeta(3).

Also equals 3rd derivative of -Pi*binomial(x, x/2) at x=0.

Example

5.6645597042446183908052136898788142322518455591949799463744298643...

Mathematica

RealDigits[(3/2)*Pi*Zeta[3], 10, 105] // First

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Sequence in context: A334381 A153415 A154010 * A217706 A064864 A004553

Adjacent sequences: A258747 A258748 A258749 * A258751 A258752 A258753

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Jun 09 2015

Status

approved