The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation

In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R^+_2=\{(x,y)\colon x>0,\ y>0\}$. They contain Kummer's confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain $\Omega\subset R^+_2$. Using the method of Green's functions, solution of this problem is found in an explicit form.