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A185578
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Decimal expansion of Sum'_{m,n,p = -infinity .. infinity} (-1)^(m + n)/sqrt(m^2 + n^2 + p^2), negated.
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8
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1, 4, 8, 0, 3, 8, 9, 8, 0, 6, 5, 1, 2, 2, 2, 2, 5, 9, 7, 9, 0, 7, 7, 6, 1, 7, 0, 6, 3, 5, 2, 8, 1, 7, 5, 5, 5, 7, 0, 7, 6, 6, 0, 5, 0, 8, 5, 1, 3, 6, 8, 8, 5, 5, 3, 6, 4, 5, 5, 3, 6, 2, 5, 7, 0, 0, 8, 7, 5, 7, 3, 1, 7, 4, 3, 5, 0, 4, 6, 1, 2, 7, 3, 9, 8, 8, 9, 1, 0, 7, 8, 8, 9, 0, 2, 0, 4, 5, 9, 0, 1, 8, 6, 7, 9
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OFFSET
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1,2
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COMMENTS
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The prime at the sum symbol means the term at m=n=p=0 is omitted.
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LINKS
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FORMULA
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Equals Pi/2 - 9*log(2)/2 + 4*Sum_{p>=1, n>=1} (1+(-1)^n+(-1)^(n+p))*cosech(d*Pi)/d where d = sqrt(n^2 + p^2).
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EXAMPLE
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1.48038980651222259790776170...
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MATHEMATICA
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digits = 105; Clear[f]; f[n_, p_] := f[n, p] = (s = Sqrt[n^2 + p^2]; ((1 + (-1)^n + (-1)^(n + p))*Csch[s*Pi])/s // N[#, digits+10]&); f[m_] := f[m] = Pi/2 - 9*Log[2]/2 + 4*Sum[f[n, p], {n, 1, m}, {p, 1, m}] // RealDigits[#, 10, digits + 10]& // First; f[0]; f[m=10]; While[ f[m] != f[m-10], Print[m]; m = m+10]; f[m][[1 ;; digits]] (* Jean-François Alcover, Feb 20 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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STATUS
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approved
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