Communications of the
Korean Mathematical Society CKMS

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\overline{H}$-function. Each of these formula involves a product of the $\overline{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\overline{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\overline{H}$-function occurring in each of main results can be reduced, under various special cases.

Keywords: generalized fractional calculus operators, fractional calculus, $\overline{H}$-function of two variables, Srivastava polynomials, special function

MSC numbers: 26A33, 33C45, 33C60, 33C70