  Two new general representations (the series and the integral) for the mass
current $\vj$ in weakly inhomogeneous superfluid A-phase of Helium--3 are
obtained near zero of temperature by solving the Dyson-Gorkov equation. These
representations result in additional correcting contribution to the standard
leading expression for $\vj$ which is of first order in gradients of the
orbital angular momentum vector $\hl$. The total supplementary term is found as
integral, and, provided the London limit holds, the procedure is advanced to
expand it at T=0 asymptotically by the Laplace method in powers of gradients of
$\hl$. Three special static orientations of $\hl$ with respect to its curl are
considered to calculate the higher correcting terms up to third order.
Coefficients at the quadratic terms are estimated numerically, new cubic
contributions are found which contain the logarithm of the London parameter.
