Geodesic
Two approaches to the~asymptotics of the~zeros of a~class of hypergeometric-type polynomials
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 483-494

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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 $y_n$. 
@article{SM_1995_83_2_a11,
     author = {A. Mart{\'\i}nez and A. Sarso and R. Yan'es},
     title = {Two approaches to the~asymptotics of the~zeros of a~class of hypergeometric-type polynomials},
     journal = {Sbornik. Mathematics},
     pages = {483--494},
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     volume = {83},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_2_a11/}
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A. Martínez; A. Sarso; R. Yan'es. Two approaches to the~asymptotics of the~zeros of a~class of hypergeometric-type polynomials. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 483-494. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a11/