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Decimal expansion of Pi*sech(Pi/2)/2.
3

%I #16 Aug 10 2020 09:28:39

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

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

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

%N Decimal expansion of Pi*sech(Pi/2)/2.

%F Equals Product_{k>=1} 1/(1 - (-1)^k/k^2).

%F Equals Product_{k>=1} (1 - 1/(2*k*(k + 1) + 1)).

%F Equals Product_{k>=1} (1 - 1/A001844(k)).

%F Equals Integral_{x=0..oo} cos(x)/cosh(x) dx. - _Amiram Eldar_, Aug 10 2020

%e 0.6260201656260738115441714982163444307583577855917...

%t RealDigits[Pi Sech[Pi/2]/2, 10, 120][[1]]

%o (PARI) Pi*(1/cosh(Pi/2))/2 \\ _Michel Marcus_, Jun 20 2019

%Y Cf. A000290, A001844, A090986, A308714, A308717.

%K nonn,cons

%O 0,1

%A _Ilya Gutkovskiy_, Jun 19 2019