## Generalized fractional integration of the $$\overline{H}$$-function.(English)Zbl 1257.26005

Summary: We study and develop the generalized fractional integral operators given by Saigo. First, we establish two theorems that give the images of the product of H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

### MSC:

 26A33 Fractional derivatives and integrals 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33C60 Hypergeometric integrals and functions defined by them ($$E$$, $$G$$, $$H$$ and $$I$$ functions) 33C70 Other hypergeometric functions and integrals in several variables
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