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A258750
Decimal expansion of Ls_4(Pi), the value of the 4th basic generalized log-sine integral at Pi.
11
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
OFFSET
1,1
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
RealDigits[(3/2)*Pi*Zeta[3], 10, 105] // First
CROSSREFS
Cf. A258749 (Ls_3(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).
Sequence in context: A334381 A153415 A154010 * A217706 A064864 A004553
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved