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

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

Offset

1,2

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Formula

Equals 1/2 + ( Pi/sqrt(2) ) /tanh( Pi/sqrt(2) ) /2.

Equals 1 + Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/2^k. - Amiram Eldar, Jun 17 2023

Example

1.6371602671179672464372644958005735739372633684506946192622824199...

Mathematica

RealDigits[1/2 + Pi/Sqrt[2]/Tanh[Pi/Sqrt[2]]/2, 10, 90][[1]]

Prog

(PARI) sumnumrat(1/(2*x^2+1), 0) \\ Charles R Greathouse IV, Jan 20 2022
(PARI) 1/2 + Pi/sqrt(2)/tanh(Pi/sqrt(2))/2 \\ Charles R Greathouse IV, Jan 20 2022

Crossrefs

Cf. A072691 (Sum_{i>=1} (1/(2*i^2))), A113319 (Sum_{i>=0} (1/(i^2+1))).

Sequence in context: A319232 A265179 A215608 * A119643 A187747 A073223

Adjacent sequences: A232880 A232881 A232882 * A232884 A232885 A232886

Keyword

nonn,cons

Author

Bruno Berselli, Dec 02 2013

Status

approved