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Hyperasymptotics for integrals with finite endpoints. (English) Zbl 0773.30040
Integrals are considered of the form ${\int }_{C}g\left(z\right)exp\left[-kf\left(z\right)\right]dz$, as $k\to \infty$, where $C$ is a contour in the complex plane with one finite endpoint. Earlier work of M. V. Berry and 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.
MSC:
 30E15 Asymptotic representations in the complex domain 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 65D32 Quadrature and cubature formulas (numerical methods)