cp's OEIS Frontend

A232883 Decimal expansion of Sum_{i>=0} (1/(2*i^2+1)).

%I A232883 #20 Jun 17 2023 03:17:49
%S A232883 1,6,3,7,1,6,0,2,6,7,1,1,7,9,6,7,2,4,6,4,3,7,2,6,4,4,9,5,8,0,0,5,7,3,
%T A232883 5,7,3,9,3,7,2,6,3,3,6,8,4,5,0,6,9,4,6,1,9,2,6,2,2,8,2,4,1,9,9,2,6,6,
%U A232883 6,9,0,2,9,7,0,6,0,9,1,1,2,5,8,2,4,3,3,0
%N A232883 Decimal expansion of Sum_{i>=0} (1/(2*i^2+1)).
%H A232883 Ivan Panchenko, <a href="/A232883/b232883.txt">Table of n, a(n) for n = 1..1000</a>
%F A232883 Equals 1/2 + ( Pi/sqrt(2) ) /tanh( Pi/sqrt(2) ) /2.
%F A232883 Equals 1 + Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/2^k. - _Amiram Eldar_, Jun 17 2023
%e A232883 1.6371602671179672464372644958005735739372633684506946192622824199...
%t A232883 RealDigits[1/2 + Pi/Sqrt[2]/Tanh[Pi/Sqrt[2]]/2, 10, 90][[1]]
%o A232883 (PARI) sumnumrat(1/(2*x^2+1), 0) \\ _Charles R Greathouse IV_, Jan 20 2022
%o A232883 (PARI) 1/2 + Pi/sqrt(2)/tanh(Pi/sqrt(2))/2 \\ _Charles R Greathouse IV_, Jan 20 2022
%Y A232883 Cf. A072691 (Sum_{i>=1} (1/(2*i^2))), A113319 (Sum_{i>=0} (1/(i^2+1))).
%K A232883 nonn,cons
%O A232883 1,2
%A A232883 _Bruno Berselli_, Dec 02 2013