A number of plane inviscid jet flow problems of interest in hydrodynamics require the use of elliptic functions theory. Generally speaking, finding the general solution to a problem in terms of elliptic functions is not a complicated task. However, finding solutions as rapidly convergent infinite series or as sound asymptotic formulas is often not as easy, and special ways of treatment may prove to be necessary. In parallel with solving the problem of peripheral jets, the author's earlier paper (1985) proposed some such ways of treatment. In the present paper, a new method of treatment is proposed (and used);this approach may be of help in studies where the methods of elliptic functions theory have to be used.