  By making use of some techniques based upon certain inverse new pairs of
symbolic operators, the author investigate several decomposition formulas
associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3
$, $\Psi_1 $, $\Psi_2 $, $\Xi_1 $ and $\Xi_2 $. 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 34 decomposition formulas are found. Euler type
integrals, which are connected with Humbert's functions are found.
