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Zeros of a certain class of Gauss hypergeometric polynomials. (English) Zbl 07031694
Summary: We prove that as \(n\to\infty\), the zeros of the polynomial \[ _2F_1\left [\begin{matrix} -n,\alpha n+1\\ \alpha n+2\end{matrix} ;z\right] \] cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter \(\alpha\) and partially proves a conjecture made by the authors in an earlier work.

MSC:
33C05 Classical hypergeometric functions, \({}_2F_1\)
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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