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

摘要

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∫evw(z)φ(z)dzfrom a well‐isolated saddle pointz0. Here v is a large positive parameter, andw(N)(z0) ≠ 0 while lower‐order derivatives atz0are equal to zero. Examples where the formulae are helpful are p