Geodesic
Zeros of a certain class of Gauss hypergeometric polynomials
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1021-1031
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We prove that as $n\to \infty $, the zeros of the polynomial $$ _{2}{F}_{1}\left [ \begin {matrix} -n, \alpha n+1\\ \alpha n+2 \end {matrix} ; z\right ] $$ 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.
We prove that as $n\to \infty $, the zeros of the polynomial $$ _{2}{F}_{1}\left [ \begin {matrix} -n, \alpha n+1\\ \alpha n+2 \end {matrix} ; z\right ] $$ 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.
DOI : 10.21136/CMJ.2018.0055-17
Classification : 30C15, 33C05
Keywords: asymptotic zero-distribution; hypergeometric polynomial; saddle point method 
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Abathun, Addisalem; Bøgvad, Rikard. Zeros of a certain class of Gauss hypergeometric polynomials. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1021-1031. doi: 10.21136/CMJ.2018.0055-17

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