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An Asymptotic Expansion of $W_{k,m}(z)$ with Large Variable and Parameters

R. Wong
Mathematics of Computation
Vol. 27, No. 122 (Apr., 1973), pp. 429-436
DOI: 10.2307/2005633
Stable URL: http://www.jstor.org/stable/2005633
Page Count: 8
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An Asymptotic Expansion of $W_{k,m}(z)$ with Large Variable and Parameters
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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 $z \rightarrow \infty$. Here, it is assumed that $k$ and $m$ are real and $|\arg z| \leqq \pi - \delta$.

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