A new class of Gould-Hopper-Eulerian-type polynomials

Abstract

In the present research work, two considerable special polynomials, Gould-Hopper polynomials and Eulerian-type polynomials are coalesced to introduce the parametric kinds of Gould-Hopper-Eulerian-type polynomials. Utilizing the operational method, the generating functions, series expansions, and differential equations for these polynomials are constructed. Various considerable identities and relations related to these polynomials are also derived. In addition, certain members of the parametric kinds of Gould-Hopper-Eulerian-type polynomials are presented and the corresponding results related to these members are derived. Further, with the help of computer-program (Mathematica), certain interesting zeros and graphical representations of some members of parametric kinds of Gould-Hopper-Eulerian-type family are presented.

Keywords

• gould-hopper polynomials
• eulerian-type polynomials
• monomiality principle
• generating function
• apostol–type polynomials