ar X iv : h ep - l at / 9 31 20 32 v 1 7 D ec 1 99 3 1 Hopping Parameter

We study leptonic and semi-leptonic decays of D and B mesons. Use of the Hopping Parameter Expansion (HPE) for two-point functions allows us continuously to vary the pseudoscalar mass from below mD up towards mB. We compute the pseudoscalar decay constants fD and fB, and observe consistency with the value calculated in the static limit. From the measurement of three-point functions we compute the matrix element relevant to the decay ¯ B → Dl¯ ν l and extract the Isgur-Wise function ξ(v.v ′). The HPE enables us freely to vary the initial state pseudoscalar mass at constant v.v ′ , and we investigate the 1/mQ corrections to the heavy-quark limit.