A family of trivariate Gould-Hopper-Bell-Apostol-Type polynomials: Construction and properties

In this study, we define and investigate a new hybrid family of special polynomials, named the trivariate Gould-Hopper-Bell-Apostol-type polynomials. By applying the monomiality principle, we construct their generating function, derive series representations, identify quasi-monomial operators, and formulate the corresponding differential equation. We also establish summation formulas and integral/differential representations. Furthermore, we investigate specific members of this family, including Gould-Hopper-Bell-Apostol-Bernoulli, Gould-Hopper-Bell-Apostol-Euler, and Gould-Hopper-Bell-Apostol-Genocchi polynomials, revealing analogous results for each. Finally, we utilize Mathematica for computational exploration, examining zero distributions and graphical representations.