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We give a pedagogical discussion of the physics underlying dispersionrelation-derived parameterizations of form factors describing B -> pi l nu andB -> D l nu. Moments of the dispersion relations are shown to providesubstantially tighter constraints on the f_+ (t) form factor describing B -> pil nu than the unweighted dispersion relation alone. Heavy quark spin symmetryrelations between the B -> pi l nu and B^* -> pi l nu form factors enables suchconstraints to be tightened even further.Comment: 18 pages, Latex, three eps figures include

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Analyticity, shapes of semileptonic form factors, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mi>l</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow></mml:math>

Analyticity, shapes of semileptonic form factors, andB¯→πlν¯