A330864 Decimal expansion of sinh(Pi/2)/2.

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, 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, 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

Offset

1,3

Comments

This constant is transcendental.

Links

Table of n, a(n) for n=1..110.

Index entries for transcendental numbers

Formula

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

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

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

Example

(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...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A153458 A096287 A240243 * A144483 A098403 A353876

Adjacent sequences: A330861 A330862 A330863 * A330865 A330866 A330867

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Apr 28 2020

Status

approved