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Keywords:
asymptotic zero-distribution; hypergeometric polynomial; saddle point method
asymptotic zero-distribution; hypergeometric polynomial; saddle point method
Summary:
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.
References:
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