Stationary Phase

I(~) = 1" ei~/(s)g(x) dx. (50.1) Through an appropriate change of variables, it can be shown (in nondegenerate cases) that J(~) -+ 0 as ~-+ oo. The maximum contributions to (50.1) will come from regions where the integrand is less oscillatory. These regions are specified by the stationary points of the integrand, that is, where J'(x) = 0.