Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu

We give a pedagogical discussion of the physics underlying dispersion relation-derived parameterizations of form factors describing B -> pi l nu and B -> D l nu. Moments of the dispersion relations are shown to provide substantially tighter constraints on the f_+ (t) form factor describing B -> pi l nu than the unweighted dispersion relation alone. Heavy quark spin symmetry relations between the B -> pi l nu and B^* -> pi l nu form factors enables such constraints to be tightened even further.