The convergence of a sequence of polynomials and the distribution of their zeros

Min-Hee Kim, Young-One Kim, Jungseob Lee

Suppose that $⟨f_n⟩$ is a sequence of polynomials, $⟨f_n^{(k)}(0)⟩$ converges for every non-negative integer $k$, and that the limit is not $0$ for some…