A368547 Decimal expansion of the Wolf-Kawalec constant of index 1.

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

Table of n, a(n) for n=0..104.

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

Cf. A000796, A001620, A073002, A074962, A082633, A201994, A368551, A368568.

Sequence in context: A200594 A319191 A124795 * A346560 A084459 A093095

Adjacent sequences: A368544 A368545 A368546 * A368548 A368549 A368550

Keyword

nonn,cons

Author

Artur Jasinski, Dec 30 2023

Status

approved