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A259281
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Decimal expansion of Sum'_{(x,y,z)=-infinity..infinity} 1/(x^2+y^2+z^2)^2, where the 'prime' indicates that the term x=y=z=0 is to be left out.
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1
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1, 6, 5, 3, 2, 3, 1, 5, 9, 5, 9, 7, 6, 1, 6, 6, 9, 6, 4, 3, 8, 9, 2, 7, 0, 4, 5, 9, 2, 8, 8, 7, 8, 5, 1, 7, 4, 3, 8, 3, 4, 1, 2, 9, 0, 7, 0, 2, 5, 5, 1, 8, 6, 8, 8, 6, 1, 1, 7, 7, 9, 3, 6, 5, 9, 5, 6, 0, 2, 7, 0, 3, 0, 9, 4, 9, 5, 1, 0, 8, 5, 2, 3, 0, 7, 7, 8
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OFFSET
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2,2
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LINKS
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M. Kontsevich and D. Zagier, Periods, Institut des Hautes Etudes Scientifiques 2001 IHES/M/01/22 p. 25.
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EXAMPLE
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16.532315959761669643892704592887851743834129...
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MATHEMATICA
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(* This script gives only 10 correct digits *) s1 = NSum[(-2 + Pi*x*(Coth[Pi*x] + Pi*x*Csch[Pi*x]^2))/(4*x^4), {x, 1, Infinity} ]; s2 = NSum[-((Csch[Pi*x]^2*(2 + 2*Pi^2*x^2 - 2*Cosh[2*Pi*x] + Pi*x*Sinh[2*Pi*x]))/(16*x^4)), {x, 1, Infinity} ]; f[y_?NumericQ] := NSum[(Pi*Coth[Pi*Sqrt[x^2 + y^2]])/(4*(x^2 + y^2)^(3/2)), {x, 1, Infinity} ]; s3 = NSum[f[y], {y, 1, Infinity} ]; g[y_?NumericQ] := NSum[2*((Pi^2*x^2*Csch[Pi*Sqrt[x^2 + y^2]]^2)/(4*(x^2 + y^2)^2)), {x, 1, Infinity} ]; s4 = NSum[g[y], {y, 1, Infinity} ]; s = Pi^4/15 + 12*s1 + 8*(s2 + s3 + s4); RealDigits[s, 10, 10] // 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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