Decomposition formulas associated with the Lauricella multivariable hypergeometric functions

By making use of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Lauricella’s hypergeometric functions FB(r),FC(r), and FD(r) in rr variables. In the three-variable case when r=3r=3, some of these operational representations are constructed and applied in order to derive the corresponding decomposition formulas. With the help of these inverse pairs of symbolic operators, a total of 15 decomposition formulas are found, which are expressed as products of hypergeometric functions of the Gauss and Appell types.