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Unified fractional integral formulae for the Fox-Wright generalized hypergeometric function. (English. Arabic summary) Zbl 1207.26015

Summary: The object of this article is to evaluate two unified fractional integrals involving the product of the Fox-Wright generalized hypergeometric function \(_p\psi_q\), the Appell function \(F_3\) and a general class of multivariable polynomials. These integrals are further applied in proving two theorems on Saigo-Maeda operators of fractional integration. The results obtained provide unification and extension of the results given earlier by Saigo, Saigo and Kilbas, Saxena and Saigo, and others. The results are obtained in a compact form and are useful in preparing some tables of Erdélyi-Kober operators, Riemann-Liouville operators, Weyl operators, Saigo operators and Saigo-Maeda operators of fractional integration.

MSC:

26A33 Fractional derivatives and integrals
33C20 Generalized hypergeometric series, \({}_pF_q\)
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