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Hyperasymptotics for Integrals with Finite Endpoints

1992
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Proceedings of the Royal Society A
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Physics L a b o r a t o r y , Tyndall , Bristol BS8 , U.K. Berry & Howls (1991) (hereinafter called BH) refined the method of steepest descent to study exponentially accurate asymptotics of a general class of integrals involving exp{-kf(z)} along doubly infinite contours in the complex plane passing over saddlepoints off(z). Here we derive analogous results for integrals with integrands of a similar form, but whose local expansions in powers of 1 are made about the finite endpoints of

doi:10.1098/rspa.1992.0156
fatcat:xcstzv73hbhnhiwi3nyjhxzi2y