OFFSET
0,1
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
EXAMPLE
0.788337023734290587067025397375...
MATHEMATICA
RealDigits[N[Coth[Pi] Pi/4, 110]][[1]]
PROG
(PARI) (Pi/4)/tanh(Pi) \\ Michel Marcus, Nov 10 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Nov 10 2020
STATUS
approved