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Explicit Series Formulae for the Evaluation of Integrals by the Method of Steepest Descents

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Explicit series formulae are given for use in the method of steepest descents, where it is required to find the contribution to an integral of the form ∫e vw(z) φ(z)dz from a well‐isolated saddle point z 0. Here v is a large positive parameter, and w (N)(z0) ≠ 0 while lower‐order derivatives at z 0 are equal to zero. Examples where the formulae are helpful are presented.
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Document Type: Research Article

Affiliations: 1: University College London 2: University of Uppsala

Publication date: October 1, 1987

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