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A258752
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Decimal expansion of Ls_6(Pi), the value of the 6th basic generalized log-sine integral at Pi.
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10
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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
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OFFSET
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3,3
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LINKS
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FORMULA
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-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.
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EXAMPLE
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119.8852400579281896736967018589288678430302320347399435542106179...
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MATHEMATICA
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RealDigits[(45/2)*Pi*Zeta[5] + (5/4)*Pi^3*Zeta[3], 10, 105] // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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