A258754 Decimal expansion of Ls_8(Pi), the value of the 8th basic generalized log-sine integral at Pi.

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

Offset

4,1

Links

Table of n, a(n) for n=4..108.

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

Formula

-Integral_{t=0..Pi} log(2*sin(t/2))^7 = (2835/4)*Pi*zeta(7) + (315/8)*Pi^3*zeta(5) + (133/32)*Pi^5*zeta(3).

Also equals 7th derivative of -Pi*binomial(x, x/2) at x=0.

Example

5040.03987911504516434562143833539315930537596167748200200213853916...

Mathematica

RealDigits[(2835/4)*Pi*Zeta[7] + (315/8)*Pi^3*Zeta[5] + (133/32)*Pi^5*Zeta[3], 10, 105] // First

Prog

(PARI) -intnum(t=0, Pi, log(2*sin(t/2))^7) \\ Hugo Pfoertner, Jul 22 2020

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)).

Sequence in context: A225424 A202626 A011995 * A175296 A076266 A350281

Adjacent sequences: A258751 A258752 A258753 * A258755 A258756 A258757

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 09 2015

Status

approved