OFFSET
0,2
FORMULA
Equals Sum_{k>=2} (k^3 -3*k^2 + k - 2)/(k^5 - k).
Equals 3/8 - 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 3/8 - Re(H(I))/2, where H is the harmonic number function.
Equals 1/4 - A338858.
Equals Sum_{k>=2} 1/(k*(k^4 - 1)). - Vaclav Kotesovec, Dec 24 2020
EXAMPLE
0.0390670072379950810608...
MATHEMATICA
Join[{0}, RealDigits[N[Re[Sum[Zeta[4 n + 1] - 1, {n, 1, Infinity}]], 105]][[1]]]
PROG
(PARI) suminf(k=1, zeta(4*k+1)-1) \\ Michel Marcus, Dec 24 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 24 2020
STATUS
approved