Some relations following from the decomposition formula for one multidimensional Lauricella hypergeometric function

Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients were constructed recently. These fundamental solutions are directly connected with multiple Lauricella hypergeometric function and the decomposition formula is required for their investigation which would express the multivariable hypergeometric function in terms of products of several simpler hypergeometric functions involving fewer variables. In this paper, some relations following from the decomposition formula for one multidimensional Lauricell hypergeometric function are determined.