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

Agarwal, Praveen

Matematiche 67, No. 2, 107-118 (2012).

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

Keywords:

fractional integral operators by Saigo; \(\overline{H}\)-function; Riemann-Liouville; Erdélyi-Kober; generalized Wright hypergeometric function; generalized Wright-Bessel function; polylogarithm function; Mittag-Leffler functions