# Nowhere stationary phase

1. Sep 20, 2011

### muppet

Hi all,
I have an integral defined as a fourier transform of the exponential of a function:
$$\mathcal{A}(\mathbf{q})=\int d^2 b e^{i \mathbf{q} \cdot \mathbf{b}}(e^{i \chi(\mathbf{b})}-1)$$
Approximating this integral via the stationary phase method (neglecting here the question of a small parameter), we look for points where
$$\frac{d\chi}{db}=q$$
However, it turns out that the derivative of my function chi is bounded above, and I'm interested in values of q that exceed my maximum value of d(chi)/db. Is there anything I can say about this integral if I can't calculate it?