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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/378

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Title: The asymptotics of the generalised Hermite–Bell polynomials
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Contemporary Sciences
Keywords: Hermite-Bell polynomials
Asymptotic expansion
Uniform approximation
Extreme zeros
Issue Date: 15-Oct-2009
Publisher: Elsevier
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)Elsevier, available from DOI: 10.1016/j.cam.2009.05.031
Citation: Paris, R. B. The asymptotics of the generalised Hermite–Bell polynomials. Journal of Computational and Applied Mathematics. 232(2): pp.216-226. Available from: DOI: 10.1016/j.cam.2009.05.031
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.
URI: http://hdl.handle.net/10373/378
ISSN: 0377-0427
Appears in Collections:Science Engineering & Technology Collection

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