Zeros of a Certain Class of Gauss Hypergeometric Polynomials

We prove that as n → ∞, the zeros of the polynomial

$$_2 F_1 left[ {begin{array}{*{20}c}{ - n,alpha n + 1} {alpha n + 2} end{array} ;z} right]$$

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 α and partially proves a conjecture made by the authors in an earlier work.