Uniform Airy-type expansions of integrals
SIAM Journal on Mathematical Analysis - Special issue: the articles in this issue are dedicated to Richard Askey and Frank Olver
Strong asymptotics of the generating polynomials of the stirling numbers of the second kind
Journal of Approximation Theory
Weak asymptotics for the generating polynomials of the stirling numbers of the second kind
Journal of Approximation Theory
Uniform asymptotic expansions of the Pollaczek polynomials
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Asymptotic analysis of the Bell polynomials by the ray method
Journal of Computational and Applied Mathematics
Uniform asymptotic expansions of the Pollaczek polynomials
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
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 {Zk}∞1⊂ (-e, 0) such that the polynomials are represented by a finite sum of infinite asymptotic series, each in term of the Airy function and its derivative, and the number of series under this sum is 1 in the interval (-∞, Z1) and k + 1 in [Zk, Zk+1), k ≥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 (-∞, -δ] for positive δ.