FRACTIONAL CALCULUS FORMULAS INVOLVING H̄ -FUNCTION AND SRIVASTAVA POLYNOMIALS

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the H̄ -function. Each of these formula involves a product of the H̄ -function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables H̄ -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 H̄ -function occurring in each of main results can be reduced, under various special cases.