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Zbl 0773.30040
Howls, C.J.
Hyperasymptotics for integrals with finite endpoints. (English)
[J] Proc. R. Soc. Lond., Ser. A 439, No.1906, 373-396 (1992). ISSN 0080-4630

Integrals are considered of the form $\int\sb C g(z)\exp[-kf(z)]dz$, as $k\to\infty$, where $C$ is a contour in the complex plane with one finite endpoint. Earlier work of {\it M. V. Berry} and {\it C. J. Howls} [Proc. R. Soc. Lond., Ser. A 434, No. 1892, 657-675 (1991; Zbl 0764.30031)] is continued in studying exponentially accurate asymptotics of this class of integrals; in Berry and Howls (1991) contours with no finite endpoints were considered. The new results are illustrated by application to the complementary error function and an incomplete Airy function.
[N.M.Temme (Amsterdam)]

MSC 2000:: *30E15 Asymptotic representations in the complex domain
41A60 Asymptotic problems in approximation
65D32 Quadrature formulas (numerical methods)

Keywords: asymptotic expansions of integrals; saddle point method; hyperasymptotics

Citations: Zbl 0764.30031

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