  We present the results of a quenched lattice QCD study of the coupling g_hat,
in the static heavy quark limit. After combining this with our previous results
obtained by using propagating heavy quarks with a mass around the physical
charm quark, we are able to interpolate to the b-quark sector. Our results are
g_hat_infinity = 0.48 +/- 0.03 +/- 0.11, g_hat_b = 0.58 +/- 0.06 +/- 0.10, and
g_Bstar_ B_p = 47 +/- 5 +/- 8.
