Asymptotic Expansions by the Method of Stationary Phase

Compared with (14.01), however, two major complications arise. First, direct integration of the terms in the expansion of f(v) over the interval (0, m) is permissible only for the first few. This is because I," e'""va-' dv diverges when a >, 1. Secondly, the upper limit b contributes to the final asymptotic expansion when p(b) is finite, whether or not t = b is a stationary point.