# New decomposition formulas associated with the Lauricella multivariable hypergeometric functions

## TL;DR

This paper refines decomposition formulas for Lauricella multivariable hypergeometric functions, making them more practical for applications, and demonstrates their use in solving boundary value problems for multidimensional elliptic equations with singular coefficients.

## Contribution

It introduces simplified and more convenient decomposition formulas for Lauricella functions and applies them to boundary value problems with singular coefficients.

## Key findings

- New, simplified expansion formulas for Lauricella functions
- Application of formulas to multidimensional elliptic boundary value problems
- Enhanced tools for solving complex differential equations

## Abstract

Decomposition formulas associated with the Lauricella multivariable hypergeometric functions were known, however, due to the recurrence of those formulas, additional difficulties may arise in the applications. Further study of the properties of the famous expansion formulas showed that it can be reduced to a more convenient form. In addition, this paper contains applications of new expansion formulas to the solving of boundary value problems for a multidimensional elliptic equation with several singular coefficients.