A338815 Decimal expansion of (Pi/4)*coth(Pi).

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

Offset: 0

Author

Artur Jasinski, Nov 10 2020

Keywords

• nonn
• cons

Examples

			0.788337023734290587067025397375...
		

Crossrefs

Cf. A338851.

Programs

Mathematica

RealDigits[N[Coth[Pi] Pi/4, 110]][[1]]

PARI

(Pi/4)/tanh(Pi) \\ Michel Marcus, Nov 10 2020

Formula

Equals (7/8) - Sum_{n>=1} (zeta(4*n)-1).

Equals (1/8) + Sum_{n>=0} (zeta(4*n+2)-1).

Equals (1/4) * (2 + i*(Psi(0,2-i) - Psi(0,2+i))), where Psi(n,x) is the n-th polygamma function and i=sqrt(-1).

Equals Sum_{k>=1} k^2/(k^4 + 4). - Amiram Eldar, Oct 04 2021