A uniform asymptotic expansion of the single variable Bell polynomials

作者：Zhao; YQ

来源：Journal of Computational and Applied Mathematics, 2003, 150(2): 329-355.

DOI：10.1016/S0377-0427(02)00669-6

• single variable Bell polynomials
• airy function
• uniform asymptotic expansion

In this paper, we investigate the uniform asymptotic behavior of the single variable Bell polynomials on the negative real axis, to which all zeros belong. It is found that there exists an ascending sequence {Z(k)}(1)(infinity) subset of (-e,0) such that the polynomials are represented by a finite sum of infinite asymptotic series, each in terms of the Airy function and its derivative, and the number of series under this sum is 1 in the interval (-infinity, Z(1)) and k 1 in [Z(k),Z(k 1)), k greater than or equal to 1. Furthermore, it is shown that an asymptotic expansion, also in terms of Airy function and its derivative, completed with error bounds, holds uniformly in (-infinity, -delta] for positive delta.

• 出版日期2003-1-15
• 单位中山大学