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Decimal expansion of sum_(n=2..infinity) (-1)^n*zeta(n)/n^2.
3

%I #12 Sep 25 2023 05:35:39

%S 3,2,0,3,4,1,1,4,2,5,1,2,7,9,3,8,3,6,2,7,2,5,6,1,0,9,3,2,1,1,7,7,8,7,

%T 1,8,7,5,3,2,1,1,4,7,9,8,7,6,2,0,3,2,3,8,5,2,0,8,9,6,9,3,1,3,3,5,7,1,

%U 3,3,4,8,6,8,0,4,0,7,3,2,2,0,1,6,9,3,0,4,6,3,1,9,2,1,2,0,8,8,0,3

%N Decimal expansion of sum_(n=2..infinity) (-1)^n*zeta(n)/n^2.

%C Let f(k) = sum_(n=2..infinity) (-1)^n*zeta(n)/n^k, then Euler gamma is f(1) and this constant is f(2).

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>

%e 0.32034114251279383627256109321177871875321147987620323852089693133571334868...

%t RealDigits[ EulerGamma + Integrate[ LogGamma[x+1]/x, {x, 0, 1}] // N[#, 100]&, 10, 100] // First

%o (PARI) sumalt(k=2,(-1)^k*zeta(k)/k^2) \\ _Vaclav Kotesovec_, Sep 23 2023

%Y Cf. A001620, A352619, A355921, A365959.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Nov 04 2013