  In this paper, we introduce a new class of confluent hypergeometric functions
of many variables, study their properties, and determine a system of partial
differential equations that this function satisfies. It turns out that all the
fundamental solutions of the generalized Helmholtz equation with several
singular coefficients are written out through the newly introduced confluent
hypergeometric function. Using the expansion formula established here for the
confluent function, the order of the singularity of the fundamental solutions
of the elliptic equation under this consideration is determined.
