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A340350
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Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + sin(x)^2*sin(y)^2) dy dx.
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5
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4, 9, 5, 3, 1, 6, 6, 1, 8, 6, 9, 2, 1, 2, 3, 3, 6, 4, 3, 0, 2, 9, 6, 5, 0, 4, 0, 4, 1, 1, 6, 1, 0, 4, 7, 5, 8, 8, 7, 1, 7, 8, 8, 4, 1, 7, 6, 7, 9, 7, 4, 5, 1, 8, 2, 4, 6, 4, 7, 4, 5, 9, 3, 4, 1, 1, 2, 3, 7, 7, 4, 0, 6, 1, 2, 4, 7, 1, 1, 3, 6, 1, 4, 3, 4, 5, 6, 5, 3, 5, 0, 3, 2, 6, 6, 3, 7, 5, 2, 8, 7, 7, 9, 2, 3, 1
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Pi * Integral_{x=0..Pi/2} log((1 + sqrt(1 + sin(x)^2))/2) dx.
Equals limit_{n->infinity} Pi^2 * (log(A340165(n)) / (2*n^2) - log(2)).
Equals limit_{n->infinity} Pi^2 * (log(A340167(n)) / (4*n^2) - log(2)).
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EXAMPLE
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0.49531661869212336430296504041161047588717884176797451824647459341123774...
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MAPLE
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evalf(Pi * Integrate(log((1 + sqrt(1 + sin(x)^2))/2), x = 0..Pi/2), 120);
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MATHEMATICA
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RealDigits[N[Pi*Integrate[Log[(1 + Sqrt[1 + Sin[x]^2])/2], {x, 0, Pi/2}], 100]][[1]]
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PROG
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(PARI) Pi * intnum(x = 0, Pi/2, log((1 + sqrt(1 + sin(x)^2))/2))
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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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