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A368547
Decimal expansion of the Wolf-Kawalec constant of index 1.
2
2, 3, 6, 1, 5, 2, 8, 8, 6, 4, 7, 7, 1, 2, 2, 9, 7, 4, 8, 6, 0, 5, 7, 8, 2, 8, 6, 0, 6, 0, 3, 2, 6, 9, 6, 0, 1, 5, 3, 2, 2, 6, 2, 9, 7, 9, 2, 3, 3, 1, 0, 9, 7, 6, 4, 0, 7, 3, 4, 8, 4, 0, 1, 7, 0, 8, 3, 9, 1, 1, 5, 6, 4, 4, 0, 4, 1, 3, 1, 6, 5, 7, 9, 5, 2, 9, 2, 8, 6, 6, 6, 0, 5, 5, 5, 1, 3, 0, 8, 4, 0, 4, 1, 1, 8
OFFSET
0,1
COMMENTS
For the Wolf-Kawalec constant of index 0 see A368551.
For the Wolf-Kawalec constant of index 2 see A368568.
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]]
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 30 2023
STATUS
approved