login
Decimal expansion of sinh(Pi/2)/2.
1

%I #11 Apr 28 2020 17:08:36

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

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

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

%N Decimal expansion of sinh(Pi/2)/2.

%C This constant is transcendental.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Sum_{k>=1} Pi^(2*k-1)/(4^k*(2*k-1)!).

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

%F Equals (i^(-i) - i^i)/4, where i is the imaginary unit.

%e (1 + 1/2^2) * (1 - 1/3^2) * (1 + 1/4^2) * (1 - 1/5^2) * (1 + 1/6^2) * ... = (e^(Pi/2) - e^(-Pi/2))/4 = 1.15064945115364743673152001...

%t RealDigits[Sinh[Pi/2]/2, 10, 110] [[1]]

%o (PARI) sinh(Pi/2)/2 \\ _Michel Marcus_, Apr 28 2020

%Y Cf. A042972, A049006, A090986, A156648, A175615, A308715, A308716, A308718, A323983, A330865, A334401.

%K nonn,cons

%O 1,3

%A _Ilya Gutkovskiy_, Apr 28 2020