A368551 -id:A368551 - cp's OEIS frontend

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

Artur Jasinski, Dec 30 2023

For the Wolf-Kawalec constant of index 0 see A368551.

For the Wolf-Kawalec constant of index 2 see A368568.

			0.23615288647712297486...

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).

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

RealDigits[Limit[D[Zeta[x]/Zeta[2 x] - 6/(Pi^2 (x - 1)), x], x -> 1],
  10, 105][[1]]

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).

A368568 Decimal expansion of the Wolf-Kawalec constant of index 2.

Original entry on oeis.org

3, 1, 9, 3, 8, 4, 1, 2, 0, 4, 0, 8, 0, 1, 4, 2, 4, 9, 2, 4, 9, 4, 6, 5, 2, 0, 7, 0, 7, 4, 5, 7, 2, 0, 1, 5, 2, 8, 1, 6, 1, 4, 2, 9, 2, 0, 2, 4, 7, 8, 3, 7, 2, 3, 8, 7, 0, 0, 2, 3, 0, 4, 9, 0, 5, 6, 0, 1, 4, 9, 0, 5, 6, 8, 4, 2, 6, 7, 7, 1, 3, 4, 1, 4, 6, 9, 7, 4, 3, 2, 4, 1, 1, 1, 4, 4, 5, 1, 9, 0, 6, 0, 2, 6, 5

Offset: 0

Artur Jasinski, Dec 30 2023

For the Wolf-Kawalec constant of index 0 see A368551.

For the Wolf-Kawalec constant of index 1 see A368547.

			0.3193841204080142492494652...

Artur Kawalec, On the series expansion of a square-free zeta series, arXiv:2312.16811 [math.NT], 2023 see Table 1.
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).

Cf. A001620, A073002, A086279, A201994, A368547, A368551.

RealDigits[Limit[D[D[Zeta[x]/Zeta[2 x] - 6/(Pi^2 (x - 1)), x], x], x -> 1],10,105][[1]]

Equals 6*(Pi^6*gamma_2 - 3456*(zeta'(2))^3 + 288*Pi^2*zeta'(2)*(gamma*zeta'(2) + 2*zeta''(2)) + 8*Pi^4*(3*gamma_1*zeta(2) - 3*gamma*zeta''(2) - 2*zeta'''(2)))/Pi^8 where gamma_2 is A086279.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula