A258752 Decimal expansion of Ls_6(Pi), the value of the 6th basic generalized log-sine integral at Pi.

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

Offset

3,3

Links

Table of n, a(n) for n=3..105.

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

Formula

-Integral_{0..Pi} log(2*sin(t/2))^5 dx = (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).

Also equals 5th derivative of -Pi*binomial(x, x/2) at x=0.

Example

119.8852400579281896736967018589288678430302320347399435542106179...

Mathematica

RealDigits[(45/2)*Pi*Zeta[5] + (5/4)*Pi^3*Zeta[3], 10, 105] // First

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Sequence in context: A256254 A203078 A065468 * A363704 A195477 A157680

Adjacent sequences: A258749 A258750 A258751 * A258753 A258754 A258755

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 09 2015

Status

approved