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Asymptotic zero distribution of hypergeometric polynomials. (English) Zbl 0935.33004
The paper is devoted to the asymptotic zero distribution of hypergeometric polynomials of the form \[ F(-n,kn+1; (k+l)n+2;z), \qquad k,l,n\in \mathbb{N}. \] The equations of the curves are given, on which the zeros lie asymptotically as \(n\to\infty\). Furthermore it is shown that for \(l=0\) the zeros cluster on the loop of a suitable lemniscate \(L_k\) as \(n\to\infty\). Similar results are presented for other functions related to hypergeometric polynomials, including Jacobi polynomials and associated Legendre functions.

MSC:
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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