We report on the MILC Collaboration's calculation of f(B), f(Bs), f(D)
, f(Ds), and their ratios. Our central values come from the quenched a
pproximation, but the quenching error is estimated from N-F = 2 dynami
cal staggered lattices. We use Wilson light valence quarks and Wilson
and static heavy quarks. for example, f(B) = 157 +/- 11(-9-0)(+25+23)
MeV, f(Bs)/f(B) = 1.11 +/- 0.02(-0.03)(+0.04) +/- 0.03, f(D), = 210 +/
- 9(-9-1)(+25+17) MeV, and f(B)/f(Ds) = 0.75 +/- 0.03(-0.02-0.00),(+0.
04+0.08) where the errors are statistical, systematic (within the quen
ched approximation), and systematic (of quenching), respectively. [S00
31-9007(98)07819-3].