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We present a recipe for constructing the effcient contour which allows one to calculate with high accuracy the Mellin-Barnes integrals, in particular, for the  F  3  structure function written in terms of its Mellin moments. We have demonstrated that the contour of the stationary phase arising for the  F  3  structure function tends to the finite limit as Re( z ) → –∞. We show that the  Q  2  evolution of the structure function can be represented as an integral over the contour of the stationary phase within the framework of the Picard-Lefschetz theory. The universality of the asymptotic contour of the stationary phase defined at some fixed value of the momentum transfer square $Q_{0}^{2}$ for calculations with any  Q  2  is shown.

High-precision numerical estimates of the Mellin-Barnes integrals for the structure functions based on the stationary phase contour