A088539 Decimal expansion of (4K/Pi)^2 where K is the Landau-Ramanujan constant.

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

Offset: 0

Author

Benoit Cloitre, Nov 16 2003

Keywords

• cons
• nonn

Examples

			0.9468064071800793342160944131097562332500695...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 100

Links

• W. Bosma and P. Stevenhagen, Density computations for real quadratic units, Math. comp. 65 (1996), 1327-1337; MR 96j : 11171.

Crossrefs

Cf. A002144, A064533, A243379, A243380. Square of A244659.

Programs

Mathematica

digits = 104; LandauRamanujanK = 1/Sqrt[2]*NProduct[((1-2^(-2^n)) * Zeta[2^n] / DirichletBeta[2^n])^(1/2^(n+1)), {n, 1, 24}, WorkingPrecision -> digits+5]; (4*LandauRamanujanK/Pi)^2 // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 04 2013, updated Mar 14 2018 *)

Formula

Equals prod(1-1/p^2) where p runs through the primes p==1 mod 4

A088539 * A243379 = 8 / Pi^2. - Vaclav Kotesovec, Apr 30 2020

Equals 1/A175647. - Vaclav Kotesovec, May 05 2020