Method of steepest descent for path integrals

To estimate path integral for a nonrelativistic particle with one degree of freedom moving in a arbitrary potential $V(x)$ it is supposed to use the pass method, being an analog of the known pass method for finite-dimensional integrals, without transferring to the euclidean formulation of the theory. The notions of the functional Cauchy–Riemann conditions and the Cauchy theorem in a complex functional space are introduced. Given a contour of the most rapid descending the initial path integral is reduced to the one with the descending exponent. In principle, this result may serve as a base to construct a path integral measure.