A258753 - OEIS

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

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OFFSET

3,1

LINKS

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

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

FORMULA

-Integral_{0..Pi} log(2*sin(t/2))^6 dx = -(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2.

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

EXAMPLE

-720.128392299770528721049702233362675341627842522005885034080645385...

MATHEMATICA