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A175296
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Decimal expansion of the absolute value of the integral of sin(Pi*x)*log(x)/x^2 from x=1 to infinity.
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0
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0, 5, 0, 4, 0, 0, 5, 9, 9, 3, 9, 7, 4, 3, 8, 8, 7, 9, 2, 2, 3, 0, 4, 1, 5, 6, 7, 7, 7, 5, 6, 4, 9, 9, 4, 8, 6, 6, 8, 6, 1, 2, 9, 4, 4, 3, 8, 1, 5, 8, 4, 3, 4, 9, 7, 9, 7, 0, 2, 0, 6, 3, 1, 6, 9, 1, 9, 4, 1, 9, 7, 4, 2, 9, 6, 1, 3, 5, 5, 0, 2, 9, 0, 0, 7, 9, 1, 8, 4, 3, 0, 7, 3, 1, 7, 1, 6, 9, 1, 2, 4, 8, 1, 3, 0
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OFFSET
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0,2
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LINKS
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EXAMPLE
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0.050400599397438879223...
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MAPLE
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evalf(Pi*(-Pi^2/24+gamma*( gamma/2+log(Pi)-1 )+log(Pi)*( log(Pi)/2-1)+1 ) -Pi^3* hypergeom([1, 1, 1], [2, 2, 2, 5/2], -Pi^2/4)/24 ) ;
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MATHEMATICA
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Join[{0}, RealDigits[N[-1/24*Pi* (Pi^2*(HypergeometricPFQ[{1, 1, 1}, {2, 2, 2, 5/2}, -Pi^2/4] + 1) + 24*(Log[Pi] - 1) - 12*(Log[Pi]^2 + EulerGamma^2 + 2*EulerGamma*(Log[Pi] - 1))), 105]][[1]]] (* Jean-François Alcover, Nov 08 2012 *)
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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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