%I
%S 4,3,5,7,5,7,0,7,6,7,7,2,6,4,5,5,9,3,7,3,7,6,2,2,9,7,0,1,2,0,9,4,1,8,
%T 6,3,4,9,6,8,6,4,1,7,4,9,2,4,3,6,8,0,3,8,1,7,5,4,6,0,9,8,9,0,9,2,3,0,
%U 0,2,3,6,0,1,6,1,0,3,0,5,3,1,8,8,0,4,3,9,7,9,5,9,7,7,2,3,4,0,6,5,3,7,6,9
%N Limit of the product of a modified Zeta function.
%C The "modified Zeta function" Zetam(n) = sum(mu(k)/k^n) may be helpful when searching for a closed form for Apery's constant.
%F Product(Sum(mu(k)/k^n)), k=1..infinity, n=2..infinity
%F Equals 1/A021002.  _R. J. Mathar_, Jan 31 2009
%e 0.43575707...
%p with(numtheory); evalf(Product(Sum('mobius(k)/k^n','k'=1..infinity),n=2..infinity),40); Note: For practical reasons you should change "infinity" to some finite value.
%p evalf(product(1/Zeta(n), n=2..infinity), 120); # _Vaclav Kotesovec_, Oct 22 2014
%t digits = 104; 1/NProduct[ Zeta[n], {n, 2, Infinity}, WorkingPrecision > digits+10, NProductFactors > 1000] // RealDigits[#, 10, digits]& // First (* _JeanFrançois Alcover_, Feb 15 2013 *)
%Y Cf. A021002, A002117.
%K cons,nonn
%O 0,1
%A Andre Neumann Kauffman (andrekff(AT)hotmail.com), Apr 01 2002
%E Corrected and extended by _R. J. Mathar_, Jan 31 2009
%E Example corrected by _R. J. Mathar_, Jul 23 2009
