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

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

Author

Artur Jasinski, Dec 30 2023

Keywords

• nonn
• cons

Comments

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

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

Examples

			0.3193841204080142492494652...
		

Links

• 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).

Crossrefs

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

Programs

Mathematica

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

Formula

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.