Zeros of a certain class of Gauss hypergeometric polynomials

Czechoslovak Mathematical Journal

Addisalem Abathun, Rikard Bøgvad¹ 

关键词: asymptotic zero-distribution;    hypergeometric polynomial;    saddle point method;   

DOI  :  10.21136/CMJ.2018.0055-17

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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.

【 授权许可】

Unknown