A330865 Decimal expansion of cosh(Pi/2)/Pi.

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

Offset: 0

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

• nonn
• cons

Examples

			(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))/(2*Pi) = 0.7986963159564630848638067...
		

Crossrefs

Cf. A042972, A049006, A049541, A156648, A175615, A308715, A308716, A308718, A323982, A330864, A334402.

Programs

Mathematica

RealDigits[Cosh[Pi/2]/Pi, 10, 110] [[1]]

PARI

cosh(Pi/2)/Pi \\ Michel Marcus, Apr 28 2020

Formula

Equals Sum_{k>=0} Pi^(2*k-1)/(4^k*(2*k)!).

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

Equals (i^(-i) + i^i)/(2*Pi), where i is the imaginary unit.