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Zbl 0851.41028
Boyd, W.G.C.
Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. (English)
[J] Methods Appl. Anal. 2, No.4, 475-489 (1995). ISSN 1073-2772

Summary: We set out two kinds of calculations for estimating the behavior of the late coefficients in the asymptotic expansions which arise in the method of steepest descents. Both are based on the reformulation of this method due to Berry and Howls. The first kind of calculation yields asymptotic expressions in which the higher-order terms diminish in inverse powers of $r$, while in the second kind of calculation, the higher-order terms diminish as in an inverse factorial series. We illustrate the calculations by applying them to the late coefficients in the asymptotic expansions of the Airy function, the modified Bessel function and the gamma function.

MSC 2000:: *41A60 Asymptotic problems in approximation
41A80 Remainders in approximation formulas

Keywords: steepest descents; Airy function; modified Bessel function; gamma function

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