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A367976 Decimal expansion of Sum_{k >= 0} (-1)^k/(1+k^2).

%I A367976 #15 Jun 10 2024 00:13:29
%S A367976 6,3,6,0,1,4,5,2,7,4,9,1,0,6,6,5,8,1,4,7,5,1,1,8,2,9,1,8,3,6,0,1,8,7,
%T A367976 7,7,9,2,0,3,5,9,1,8,1,7,3,0,1,5,7,9,7,4,7,5,3,4,4,8,3,9,1,9,2,8,1,2,
%U A367976 3,0,9,5,6,8,4,7,4,3,9,4,4,0,9,5,5,7,6,5,5,8,6,0,5,3,4,6,8,8,2,2,4,3,0,5
%N A367976 Decimal expansion of Sum_{k >= 0} (-1)^k/(1+k^2).
%F A367976 Equals (2-Pi*tanh(Pi/2)+Pi*coth(Pi/2))/4 = (1 - A228048 + Pi/2*A367961)/2.
%F A367976 From _Amiram Eldar_, Dec 11 2023: (Start)
%F A367976 Equals (1 + Pi/sinh(Pi))/2.
%F A367976 Equals Integral_{x>=0} (cos(x)/cosh(x))^2 dx. (End)
%F A367976 Equals (1+A090986)/2. - _R. J. Mathar_, Dec 13 2023
%e A367976 0.636014527491066581475118291836...
%p A367976 1/4*(2-Pi*tanh(Pi/2)+Pi*coth(Pi/2)) ; evalf(%) ;
%t A367976 RealDigits[(1 + Pi*Csch[Pi])/2, 10, 120][[1]] (* _Amiram Eldar_, Dec 11 2023 *)
%o A367976 (PARI) sumalt(k=0, (-1)^k/(1+k^2)) \\ _Michel Marcus_, Dec 07 2023
%Y A367976 Cf. A113319.
%K A367976 nonn,cons
%O A367976 0,1
%A A367976 _R. J. Mathar_, Dec 07 2023