Abstract
The Hermite–Bell polynomials are defined by [formula missing] for n=0,1,2,… and integer r≥2 and generalise the classical Hermite polynomials corresponding to r=2. We obtain an asymptotic expansion for [formula missing] as n→∞ using the method of steepest descents. For a certain value of x, two saddle points coalesce and a uniform approximation in terms of Airy functions is given to cover this situation. An asymptotic approximation for the largest positive zeros of [formula missing] is derived as n→∞. Numerical results are presented to illustrate the accuracy of the various expansions.
Original language | English |
---|---|
Pages (from-to) | 216-226 |
Number of pages | 11 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 232 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Oct 2009 |