A Generalization of the Saddle-Point Approximation Method

This paper generalizes the well-known Saddle-point approximation to integrands that are not necessarily strongly peaked. The method makes use of a technique similar to the Faddeev-Popov trick to make a decent approximation of the integral even when fluctuations are significant. This makes this method useful in Theoretical and Mathematical Physics (e.g. Quantum Field Theory or Statistical Physics) , but also for asymptotic analysis of special functions and many similar areas of research.