Subuhi Khan (Aligarh Muslim University, Aligarh, India)

Some results involving Hermite-based Appell polynomials

Abstract:
   Operational methods can be used to simplify the derivation of the properties associated with ordinary and generalized special functions and to introduce new families of special polynomials and special functions. In the case of multi-variable generalized special functions, the use of operational techniques combined with the principle of monomiality provides new means of asnalysis for the solutions of a wide class of partial differential equations often encountered in physical problems. By employing certain operational methods, the Hermite-based Appell polynomials are introduced. Some properties of Hermite-based Appell polynomials are considered which proved to be useful for the derivation of identities involving these polynomials. The possibility of extending this technique to introduce Hermite-based Sheffer polynomials (for example Hermite-Laguerre and Hermite-Sister Celine’s polynomials) is also investigated.