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Asymptotic properties of zeros of hypergeometric polynomials. (English) Zbl 0983.33008
The zeros of the hypergeometric polynomials \(F(-n, kn+1; kn+2; z)\) are considerd for any \(k>0\). It is shown that every point of a certain lemniscate is a cluster point of zeros as \(n\to\infty\). In an earlier paper by K. Driver and P. Duren [Numer. Algorithms 21, No. 1-4, 147-156 (1999; Zbl 0935.33004)] a similar study for positive integer values of \(k\) has been given.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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References:
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