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Hyperasymptotics for integrals with finite endpoints. (English) Zbl 0773.30040
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.

30E15Asymptotic representations in the complex domain
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
65D32Quadrature and cubature formulas (numerical methods)
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