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 and Armin Straub, Special values of generalized log-sine integrals, ISSAC '11: Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011, pp. 43-50; alternative link.

Formula

Equals -Integral_{0..Pi} log(2*sin(t/2))^5 dx.

Equals (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).

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

Prog

(PARI) (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3) \\ Amiram Eldar, Jun 29 2026

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 A382604

Adjacent sequences: A258749 A258750 A258751 * A258753 A258754 A258755

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Jun 09 2015

Status

approved