Appell polynomials and their zero attractors

被引:0
作者
Boyer, Robert P. [1 ]
Goh, William M. Y. [1 ]
机构
[1] Drexel Univ, Dept Math, Philadelphia, PA 19104 USA
来源
GEMS IN EXPERIMENTAL MATHEMATICS | 2010年 / 517卷
关键词
Appell polynomials; zeros of polynomials; asymptotics;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A polynomial family {p(n)(x)} is Appell if it is given by e(xt)/g(t) = Sigma(infinity)(n=0) p(n)(x)t(n) or, equivalently, p(n)'(x) = p(n-1)(x). If g(t) is an entire function, g(0) not equal 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.
引用
收藏
页码:69 / 96
页数:28
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