%0 Journal Article
%T Appell Polynomials and Their Zero Attractors
%A Robert P. Boyer William M. Y. Goh
%J Mathematics
%D 2008
%I arXiv
%X A polynomial family $\{p_n(x)\}$ is Appell if it is given by $\frac{e^{xt}}{g(t)} = \sum_{n=0}^\infty p_n(x)t^n$ or, equivalently, $p_n'(x) = p_{n-1}(x)$. If $g(t)$ is an entire function, $g(0)\neq 0$, with at least one zero, the asymptotics of linearly scaled polynomials $\{p_n(nx)\}$ are described by means of finitely zeros of $g$, including those of minimal modulus. As a consequence, we determine the limiting behavior of their zeros as well as their density. The techniques and results extend our earlier work on Euler polynomials.
%U http://arxiv.org/abs/0809.1266v1