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

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 F₃ structure function written in terms of its Mellin moments. We have demonstrated that the contour of the stationary phase arising for the F₃ structure function tends to the finite limit as Re(z) → –∞. We show that the Q² 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 for calculations with any Q² is shown.