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

Abstract

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.

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