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A259173
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Decimal expansion of the positive solution x to Sum_{k>=1} 1/(k^2 + x) = 1.
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1
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1, 2, 8, 0, 2, 0, 1, 6, 8, 3, 2, 8, 9, 5, 6, 6, 0, 1, 0, 6, 1, 2, 9, 1, 8, 8, 3, 7, 5, 7, 9, 9, 6, 4, 2, 1, 3, 1, 4, 8, 6, 1, 8, 4, 2, 4, 9, 1, 5, 8, 5, 0, 4, 2, 8, 9, 2, 2, 1, 3, 0, 5, 7, 9, 6, 1, 5, 1, 8, 6, 2, 3, 2, 7, 5, 1, 8, 6, 8, 0, 7, 7, 6, 2, 7, 2
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1.2802016832895660106129188375799642131486184249158504289221305
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MATHEMATICA
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g[n_]:=Sum[1/(k^2+n), {k, Infinity}]; x/.FindRoot[g[x]==1, {x, 1}, AccuracyGoal->2000, WorkingPrecision-> 2340, MaxIterations->1000]//RealDigits//First
FindRoot[Pi*Sqrt[x]*Coth[Pi*Sqrt[x]] == 2*x+1, {x, 1}, WorkingPrecision->120] (* Vaclav Kotesovec, Jun 28 2015 *)
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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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