This is my first post here so Hello everybody!!

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

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

when 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 f(z)=e^{th(z)}