A258753 Decimal expansion of Ls_7(Pi), the value of the 7th basic generalized log-sine integral at Pi (negated).

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

Offset

3,1

Links

Table of n, a(n) for n=3..104.

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))^6 dx.

Equals -(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2.

Equals 6th derivative of -Pi*binomial(x, x/2) at x=0.

Example

-720.128392299770528721049702233362675341627842522005885034080645385...

Mathematica

RealDigits[-(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2 , 10, 102] // First

Prog

(PARI) -(275/1344)*Pi^7 - (45/2)*Pi*zeta(3)^2 \\ Amiram Eldar, Jun 29 2026

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)),A258754 (Ls_8(Pi)).

Sequence in context: A296791 A246851 A258763 * A248363 A220674 A102771

Adjacent sequences: A258750 A258751 A258752 * A258754 A258755 A258756

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Jun 09 2015

Status

approved