The construction of the efficient contour of the inverse Mellin transformation for the F3 structure function

Abstract

We estimate the accuracy of the reconstruction of the structure function xFs (x, Q ) by the Mellin inverse transformation method using the parabolic con­tour running from a saddle point proposed by Kosower. The choice of the contour is of great practical importance. We are studying the possibility of increasing the efficiency of the parabolic contour by taking into account the higher-order terms. We demonstrate the proximity of the parabolic contour and the contour of the stationary phase.