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

## TL;DR

This paper explores relations derived from the decomposition formula of a multidimensional Lauricella hypergeometric function, aiding the analysis of fundamental solutions for certain elliptic equations with singular coefficients.

## Contribution

It identifies specific relations from the decomposition formula of a Lauricella hypergeometric function, advancing understanding of multidimensional hypergeometric functions.

## Key findings

- Derived relations from the decomposition formula for Lauricella hypergeometric functions.
- Enhanced methods for analyzing fundamental solutions of elliptic equations with singular coefficients.
- Contributed to the theoretical framework connecting hypergeometric functions and elliptic PDEs.

## Abstract

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.