Introducing a novel family of Δ h -Sheffer polynomials and their interconnected hybrid variants

‎The main objective of this work is to investigate a novel class of polynomials‎, ‎called the \(\Delta_h\)-Sheffer polynomials and to explore their various properties‎. ‎The generating function‎, ‎explicit representations‎, ‎quasi-monomiality‎, ‎and certain novel identities involving \(\Delta_h\)-Sheffer polynomials are obtained‎. ‎Also‎, ‎the \(\Delta_h\)-Sheffer polynomials are explored via determinant representation‎. ‎Further‎, ‎the \({\Delta_h}\) Gould-Hopper-Sheffer polynomials are introduced with the help of \(\Delta_h\)-Sheffer and \({\Delta_h}\) Gould-Hopper polynomials‎. ‎Certain fascinating results‎, ‎such as the generating function‎, ‎determinant form‎, ‎multiplicative‎, ‎and derivative operators and many more results for these hybrid form of the \(\Delta_h\)-Sheffer polynomials are also obtained‎. ‎Certain examples are considered as the special cases of \({\Delta_h}\) Gould-Hopper-Sheffer polynomials‎.