Some exact representations for the mass current in $^3\mathrm{He}$-$\mathrm A$ and their zero temperature implications

New representations for the mass current in the $A$-phase of helium-3 are obtained from an exact solution of the Dyson–Gor'kov equation. Expansion of these representations over powers of a small parameter which characterizes the London limit is considered. A previously known formula for the current is obtained in the main order for zero temperature. The corresponding higher terms are estimated. Bibliography: 19 titles.