## Asymptotic Expansion of an integral

This is my first post here so Hello everybody!!

Does anyone know if there is method for the asymptotic expansion of integrals like

$\displaystyle \int_C g(z)[f(z)]^t dz$

when $\displaystyle t\to \infty$ and f and are complex value and analytic functions and C is a contour?

Can I use the steeest descent / saddle point method for this? In general, all the asymptotic methods are for integrals with $\displaystyle f(z)=e^{th(z)}$