Czechoslovak Mathematical Journal, first online, pp. 1-11

Zeros of a certain class of Gauss hypergeometric polynomials

Addisalem Abathun, Rikard Bøgvad

Received February 8, 2017.   First published February 2, 2018.

Abstract:  We prove that as $n\to\infty$, the zeros of the polynomial ${}_{2}{F}_{1}\left[ \matrix -n,\al n+1\\ \al n+2 \endmatrix ;z\right]$ 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.
Keywords:  asymptotic zero-distribution; hypergeometric polynomial; saddle point method
Classification MSC:  33C05, 30C15
DOI:  10.21136/CMJ.2018.0055-17

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Affiliations:   Addisalem Abathun, Department of Mathematics, Stockholm University, Universitetsvägen 10, 114 18 Stockholm, Sweden, and Department of Mathematics, Addis Ababa University, Ras Mekonnen Bldg., P. O. Box 1176, Addis Ababa, Ethiopia, e-mail:; Rikard Bøgvad, Department of Mathematics, Stockholm University, Universitetsvägen 10, 114 18 Stockholm, Sweden, e-mail:

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