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Perturbation Methods Problem

Consider the integral

1965_notation.jpg

Where the notation is

956_notation_2.jpg

means a contour that is parallel to the real z axis, but moved down by a distance d.

Use the method of steepest descents to derive the full asymptotic expansion of I2 in the limit e → 0. You will have to treat the cases s > 0 and s < 0 separately, although much of the working is the same for each.

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