An asymptotic expansion of 𝑊_{𝑘,𝑚}(𝑧) with large variable and parameters

Wong, R.

doi:10.1090/S0025-5718-1973-0328145-7

An asymptotic expansion of $W_{k, m}(z)$ with large variable and parameters
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Math. Comp. 27 (1973), 429-436 Request permission

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 $|\arg z|\; \leqq \;\pi - \delta$.

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