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Decimal expansion of Sum_{k>=0} (-1)^k / (k^2 + 4).
2

%I #11 Apr 22 2024 13:43:51

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

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

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

%N Decimal expansion of Sum_{k>=0} (-1)^k / (k^2 + 4).

%F Equals (1/8)*(1 + 2*Pi*csch(2*Pi).

%F Equals 1/8 + Pi*exp(2*Pi)/(2*(exp(4*Pi) - 1)). - _Vaclav Kotesovec_, Apr 22 2024

%e 0.1279333824131754728739815724485566356111330...

%t s = Re[N[Sum[(-1)^k/(k^2 + 4), {k, 0, Infinity}], 120]]

%t First[RealDigits[s]]

%Y Cf. A329085.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Apr 17 2024