Asymptotics of Feynman integrals in the one-dimensional case

The asymptotics of the Feynman integrals of the form $\mathcal{F}(t)=\int\limits_{0}^{+\infty}(P(x,t))^{-\lambda}dx$ is studied for $t\rightarrow +0$. The first term of the asymptotics is calculated in the general case and a method for obtaining a complete asymptotic expansion in the case of one essential face is presented.