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A258753
Decimal expansion of Ls_7(Pi), the value of the 7th basic generalized log-sine integral at Pi (negated).
10
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
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
RealDigits[-(275/1344)*Pi^7 - (45/2)*Pi*Zeta[3]^2 , 10, 102] // First
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved