OFFSET
0,1
COMMENTS
LINKS
Artur Kawalec, On the series expansion of a square-free zeta series, arXiv:2312.16811 [math.NT], 2023.
Marek Wolf, Numerical Determination of a Certain Mathematical Constant Related to the Mobius Function, Computational Methods in Science and Technology, Volume 29 (1-4) 2023, 17-20 see formula (20).
FORMULA
Equals -(864*(zeta'(2))^2 - 72*Pi^2*(gamma*zeta'(2) + zeta''(2)) - 6*Pi^4*gamma_1)/Pi^6 where gamma_1 is A082633 negated.
Equals -(6*Pi^2*(2*(gamma + log(2) - 12*log(Glaisher) + log(Pi))*(gamma + 2*log(2) - 24*log(Glaisher) + 2*log(Pi)) - gamma_1) - 72*zeta''(2))/Pi^4 where Glaisher is the Glaisher-Kinkelin constant A (see A074962).
EXAMPLE
0.23615288647712297486...
MATHEMATICA
RealDigits[Limit[D[Zeta[x]/Zeta[2 x] - 6/(Pi^2 (x - 1)), x], x -> 1],
10, 105][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 30 2023
STATUS
approved