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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. (English) Zbl 0851.41028
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:
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A80Remainders in approximation formulas