Explicit Form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope {rho}{sup 2}=-{xi}{sup '}(1) of the Isgur-Wise (IW) function {xi}(w) attains its lower bound (3/4), then all the derivatives (-1){sup L}{xi}{sup (L)}(1) attain their lower bounds ((2L+1){exclamation_point}{exclamation_point}/2{sup 2L}), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function {xi}(w)=((2/w+1)){sup 3/2}. Since the so-called BPS condition proposed by Uraltsev implies {rho}{sup 2}=(3/4), it implies also that the IW function is given by the preceding expression.