  The double-layer potential plays an important role in solving boundary value
problems for elliptic equations, and in the study of which for a certain
equation, the properties of the fundamental solutions of the given equation are
used. All the fundamental solutions of the generalized bi-axially symmetric
Helmholtz equation were known, and only for the first one was constructed the
theory of potential. Here, in this paper, we aim at constructing theory of
double-layer potentials corresponding to the third fundamental solution. By
using some properties of one of Appell's hypergeometric functions in two
variables, we prove limiting theorems and derive integral equations concerning
a denseness of double-layer potentials.
