  By making use of some techniques based upon certain inverse new pairs of
symbolic operators, the author investigate several decomposition formulas
associated with Lauricella's hypergeometric functions $F_A^{(r)}, F_B^{(r)},
F_C^{(r)}$ and $F_D^{(r)}$ in $r$ variables. In the three-variable case some of
these operational representations are constructed and applied in order to
derive the corresponding decomposition formulas when $r = 3$ . With the help of
these new inverse pairs of symbolic operators, a total 20 decomposition
formulas and integral representations are found.
