The Hermite-Bell polynomials are defined by H r n (x) = (-) n exp(x r )(d/dx) n exp(-x r ) for n = 0, 1, 2, . . . and integer r β₯ 2 and generalise the classical Hermite polynomials corresponding to r = 2. We obtain an asymptotic expansion for H r n (x) as n β β using the method of steepest descents.
β¦ LIBER β¦
Asymptotic analysis of the Bell polynomials by the ray method
β Scribed by Diego Dominici
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 651 KB
- Volume
- 233
- Category
- Article
- ISSN
- 0377-0427
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β¦ Synopsis
We analyze the Bell polynomials B n (x) asymptotically as n β β. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.
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