OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.
LINKS
Eric Weisstein's MathWorld, Ramanujan constant
FORMULA
1/(4*K), where K is the Landau-Ramanujan constant.
EXAMPLE
0.327129366941026382400232869028392799695...
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]; 1/(4*LandauRamanujanK) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 04 2014
STATUS
approved