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Abstract
Recently developed techniques for evaluating higher-order semiclassical phase integrals are extended to allow the computation of phase integrals close to potential extrema, where the earlier procedure is numerically unstable. The new methods are required in the calculation of certain integrals encountered in double minimum and resonance scattering problems. Various distributions and ranges of the integration mesh points are studied and global recommendations for use of various versions of the general integration procedure and the choice of mesh points are given.
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