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We prove that as $n\to \infty$, the zeros of the polynomial $${}_2{F}_1\left[\begin{array}{c}-n,\alpha n+1\\ \alpha n+2\end{array};z\right]$$ 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 $\alpha$ and partially proves a conjecture made by the authors in an earlier work.

In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.