Asymptotic zero distribution of a class of hypergeometric polynomials

K. A. Driver, S. J. Johnston

We prove that the zeros of ${}_2{F}_1(-n,\frac{n+1}{2};\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\{z:|z(1-z{)}^2|=4/27;\text{Re}(z)>1/3\}$ as $n\righ…