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_∞ = 0.48±0.03±0.11, g-hat_b = 0.58±0.06±0.10, and g _B*Bπ = 47±5±8.