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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An asymptotic expansion of $ W\sb{k,\,m}(z)$ with large variable and parameters


Author: R. Wong
Journal: Math. Comp. 27 (1973), 429-436
MSC: Primary 33A30
MathSciNet review: 0328145
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Abstract: In this paper, we obtain an asymptotic expansion of the Whittaker function $ {W_{k,m}}(z)$ when the parameters and variable are all large but subject to the growth restrictions that $ k = o(z)$ and $ m = o({z^{1/2}})$ as $ z \to \infty $. Here, it is assumed that k and m are real and $ \vert\arg z\vert\; \leqq \;\pi - \delta $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0328145-7
PII: S 0025-5718(1973)0328145-7
Keywords: Whittaker function, asymptotic expansion, parabolic cylinder functions, Hankel functions
Article copyright: © Copyright 1973 American Mathematical Society