OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.
LINKS
Eric Weisstein's World of Mathematics, Ramanujan constant.
FORMULA
Equals (4/Pi^(3/2))*exp(gamma/2)*K, where gamma is the Euler-Mascheroni constant and K the Landau-Ramanujan constant.
EXAMPLE
0.732649819283832613620305823117683687363...
MATHEMATICA
digits = 103; 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/Pi^(3/2)*Exp[EulerGamma/2]*LandauRamanujanK // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 04 2014
STATUS
approved