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

Abstract: In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R_2^ + = \left{ {\left( {x,y} \right):x > 0,y > 0} \right}.$ 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.