New Generating Functions for a Class of Generalized Hermite Polynomials

Abstract

The main object of this paper is to present several (presumably new) families of linear, bilinear, and mixed multilateral generating functions for a certain interesting generalization of the classical Hermite (and Laguerre) polynomials. Some of these generating functions are associated with the Stirling numbers of the second kind. Numerous known or new consequences of the results derived here also considered.

Fractional integral operators involving the product of Srivastava polynomials and Srivastava-Panda multivariable $ H $ -functions of generalized arguments

“…In recent years several authors (see, for example) Chen et al [13], Lin et al [16], Soni et al [15], seee also Gaira et al [12] have made significant contributions to the fractional calculus operators involving various functions and polynomials. Here we are making an attempt to develop extensions of these results.…”

Fractional integral formulae concerning certain special functions

“…From the last four decades several mathematician (see, for example Ross [2], Kilbas and Saigo [1], Srivastava and Goyal [12], Srivastava and Hussain [6], Srivastava, Chandel and Vishwakarma [10], Manocha and Sharma [3], Saigo and Raina [17], Dhami and Gaira [15], Lin, Tu and Srivastava [19], Oldham and Spanier [13], Chaurasia and Godika [21], and Chaurasia and Gupta [20]) have made great and significant contribution in the field of fractional calculus, specially fractional derivatives and fractional integrals involving various functions.…”