The Liouville-Stekloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation are used in order to improve a classical asymptotic formula for the gr
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Asymptotics of the Zeros of Relativistic Hermite Polynomials
β Scribed by He, Matthew; Pan, K.; Ricci, Paolo E.
- Book ID
- 118200160
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1997
- Tongue
- English
- Weight
- 248 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0036-1410
No coin nor oath required. For personal study only.
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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.