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By making use of some techniques based upon certain inverse new pairs ofsymbolic operators, the author investigate several decomposition formulasassociated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3$, $\Psi_1 $, $\Psi_2 $, $\Xi_1 $ and $\Xi_2 $. These operationalrepresentations are constructed and applied in order to derive thecorresponding decomposition formulas. With the help of these inverse pairs ofsymbolic operators, a total 34 decomposition formulas are found. Euler typeintegrals, which are connected with Humbert's functions are found.

Applications of the operator $H(\alpha,\beta)$ to the Humbert double hypergeometric functions