Take the 2-minute tour ×  I have this question at MO and I would
like to know if we can give hints to get the symbolic sums and
products to come out as $\frac{6}{\pi^{2}}\pm\epsilon$ instead
of $0.60792710...$ accurate to $\epsilon$.  ε = 0.000000001; s =
0; Sum[(MoebiusMu[n] + ε)/n^s, {n, 1, ∞}] /
Product[n^(MoebiusMu[n] ε), {n, 1, ∞}] == 1/Zeta[s] + ε    When
$s=0$ we get $-2\pm\epsilon$, but we have to use NSum. When
$s=2$ or greater, we get the decimal expansion and I would like
to see the zeta values $\pm\epsilon$.  Can we do this?
share|improve this question add comment  1 Answer  up vote 1
down vote accepted  I just created a wrapper for the generating
function of the LHS.  mcalc[s_,ε_] := {1/Zeta[s], 1/Zeta[s] - (2
π)^(2 ε) (1 + ε Zeta[s]^2)/Zeta[s]} mcalc[2, 0.000000000001]
(* {6/π^2, -3.87945*10^-12} *) share|improve this answer add
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