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A new approximation is proposed for the contour of the stationary phase ofthe Mellin--Barnes integrals in the case of its finite asymptotic behavior as${\rm Re} z\to -\infty$. The efficiency of application of the proposed contourand the quadratic approximation to the contour of the stationary phase iscompared by the example of the inverse Mellin transform for the structurefunction $F_3$. It is shown that, although for a small number of terms $N$ inquadrature formulas used to calculate integrals along these contours, thequadratic contour is more efficient, but for $N>20$ the asymptotic stationaryphase integration contour gives better accuracy. The case of the$Q^2$-dependence of the $F_3$ structure function is also considered.

Asymptotics of the contour of the stationary phase and efficient evaluation of the Mellin-Barnes integral for the F_3 structure function