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A247508
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Decimal expansion of L_2 = -Integral_{x=0..Pi/2} log(2*sin(x/2))^2 dx, a constant appearing in the evaluation of Euler double sums not expressible in terms of well-known constants.
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0
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2, 0, 3, 3, 5, 7, 6, 5, 0, 6, 0, 7, 2, 0, 5, 4, 6, 0, 0, 9, 1, 2, 0, 6, 8, 9, 6, 9, 7, 0, 0, 5, 1, 8, 2, 4, 9, 9, 9, 2, 3, 7, 6, 0, 7, 5, 6, 1, 3, 0, 4, 6, 1, 8, 5, 5, 0, 6, 4, 8, 7, 4, 2, 9, 8, 5, 8, 4, 3, 9, 6, 8, 9, 6, 8, 6, 9, 1, 5, 1, 2, 3, 5, 5, 5, 4, 1, 1, 6, 3, 3, 0, 6, 5, 9, 6, 3, 2, 0, 0
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OFFSET
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1,1
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LINKS
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FORMULA
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L_2 = -Pi^3/24 - (1/2)*Sum_{m >= 1} (Sum_{n=1..m} ((-1)^(n-1)/(2*n-1))/m^2).
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EXAMPLE
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-2.0335765060720546009120689697005182499923760756130461855 ...
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MAPLE
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evalf(-Pi^3/24 - (1/2)*sum(sum((-1)^(n-1)/(2*n-1)/m^2, n=1..m), m=1..infinity), 100) # Vaclav Kotesovec, Sep 18 2014
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MATHEMATICA
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digits = 100; L2 = -NIntegrate[Log[2*Sin[t/2]]^2, {t, 0, Pi/2}, WorkingPrecision -> digits+10]; RealDigits[L2, 10, digits] // 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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