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A091349
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Decimal expansion of Sum_{m>=1, n>=1} 1/(m^2*(m^2 + m*n + n^2)).
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0
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1, 0, 0, 4, 4, 5, 7, 1, 9, 8, 2, 0, 1, 5, 7, 4, 0, 2, 7, 5, 5, 4, 1, 4, 0, 2, 5, 6, 6, 9, 4, 0, 2, 6, 0, 0, 2, 9, 1, 6, 6, 9, 3, 4, 9, 4, 2, 1, 7, 1, 9, 6, 6, 6, 4, 6, 2, 5, 7, 5, 6, 5, 9, 2, 0, 3, 2, 1, 6, 8, 6, 0, 0, 6, 2, 3, 3, 9, 2, 3, 7, 0, 8, 2, 5, 2, 0, 6, 1, 1, 1, 0, 5, 3, 5, 8, 1, 6, 0, 4
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OFFSET
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1,4
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LINKS
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EXAMPLE
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1.0044...
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MATHEMATICA
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digits = 100; Pi^4/36 - EulerGamma*Zeta[3] + NSum[ (-3 - I*Sqrt[3])/6*PolyGamma[(2 + n - I*Sqrt[3]*n)/2]/n^3 + (-3 + I*Sqrt[3])/6*PolyGamma[(2 + n + I*Sqrt[3]*n)/2]/n^3, {n, 1, Infinity}, NSumTerms -> digits + 20, WorkingPrecision -> digits + 20, AccuracyGoal -> digits + 20, PrecisionGoal -> digits + 20, Method -> {"EulerMaclaurin", Method ->{"NIntegrate", "MaxRecursion" -> 20}}] // Re // RealDigits[#, 10, digits] & // First (* Jean-François Alcover, Feb 11 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
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STATUS
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approved
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