OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.
LINKS
Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See page 5.
Eric Weisstein's MathWorld, Ramanujan constant
FORMULA
2*K/Pi, where K is the Landau-Ramanujan constant (A064533).
EXAMPLE
0.4865198883858909971272456405868234...
MATHEMATICA
digits = 101; 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]; 2*LandauRamanujanK/Pi // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 04 2014
STATUS
approved