Two approaches to the asymptotics of the zeros of a class of hypergeometric-type polynomials

A class of hypergeometric-type differential equations is considered. It is shown that its polynomial solutions $y_n$ exhibit an orthogonality with respect to a ‘varying measure’ (a sequence of measures) on $\mathbb R$. From this relation the asymptotic distribution of zeros is obtained by means of a potential theory approach. Moreover, the WKB or semiclassical approximation is used to construct an asymptotically exact sequence of absolutely continuous measures that approximate the zero distribution of $y_n$.