Appell Polynomials and Their Zero Attractors

Details Appell Polynomials and Their Zero Attractors Appell Polynomials and Their Zero Attractors

2008-09-08

arxiv.org/abs/0809.1266v1

Mathematics

Combinatorics

23 pages, 9 Figures

Scientific paper

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.

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