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A258752
Decimal expansion of Ls_6(Pi), the value of the 6th basic generalized log-sine integral at Pi.
10
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
FORMULA
-Integral_{0..Pi} log(2*sin(t/2))^5 dx = (45/2)*Pi*zeta(5) + (5/4)*Pi^3*zeta(3).
Also 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
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 A157680
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved