OFFSET
0,1
COMMENTS
For additional comments and generalization see A339604.
FORMULA
Equals Sum_{k>=2} k/(k^4-1).
Equals -1/8 + gamma/2 + Re(Psi(i))/2, where Psi is the digamma function, gamma is the Euler-Mascheroni constant (see A001620), and i=sqrt(-1).
Equals -1/8 + Re(H(I))/2, where H is the harmonic number function.
EXAMPLE
0.2109329927620049189391952864...
MATHEMATICA
RealDigits[N[Re[Sum[Zeta[4 n + 3] - 1, {n, 0, Infinity}]], 105]][[1]]
PROG
(PARI) suminf(k=0, zeta(4*k+3)-1) \\ Michel Marcus, Dec 24 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 24 2020
STATUS
approved