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A185576
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Decimal expansion of Born's basic potential Pi_0.
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8
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2, 8, 3, 7, 2, 9, 7, 4, 7, 9, 4, 8, 0, 6, 1, 9, 4, 7, 6, 6, 6, 5, 9, 1, 7, 1, 0, 4, 6, 0, 7, 7, 3, 8, 8, 2, 2, 3, 8, 9, 2, 1, 8, 7, 0, 2, 1, 5, 8, 4, 8, 3, 5, 9, 9, 0, 0, 3, 7, 1, 9, 0, 0, 6, 9, 9, 9, 2, 4, 7, 7, 1, 1, 1, 6, 2, 2, 7, 3, 3, 0, 9, 4, 7, 4, 0, 4, 1, 5, 3, 0, 7, 9, 2, 7, 1, 1, 0, 3, 5
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OFFSET
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1,1
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COMMENTS
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Decimal expansion of Sum'_{m,n,p = -infinity..infinity} 1/(m^2 + n^2 + p^2)^s, analytic continuation to s=1/2. The prime at the sum symbol means the term at m=n=p=0 is omitted.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 79.
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LINKS
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FORMULA
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EXAMPLE
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2.8372974794806194766659171046...
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MATHEMATICA
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digits = 100; k0 = 10; dk = 10; Clear[s]; s[k_] := s[k] = 7*(Pi/6) - 19/2*Log[2] + 4*Sum[(3 + 3*(-1)^m + (-1)^(m + n)) * Csch[Pi*Sqrt[m^2 + n^2]]/Sqrt[m^2 + n^2], {m, 1, k}, {n, 1, k}] // N[#, digits + 10] &; s[k0]; s[k = k0 + dk]; While[RealDigits[s[k], 10, digits + 5][[1]] != RealDigits[s[k - dk], 10, digits + 5][[1]], Print["s(", k, ") = ", s[k]]; k = k + dk]; RealDigits[s[k], 10, digits] // First (* Jean-François Alcover, Sep 10 2014 *)
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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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