A258750 - OEIS

A258750

Decimal expansion of Ls_4(Pi), the value of the 4th basic generalized log-sine integral at Pi.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

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

Also equals 3rd derivative of -Pi*binomial(x, x/2) at x=0.

EXAMPLE

5.6645597042446183908052136898788142322518455591949799463744298643...

MATHEMATICA