Dunkl Transform of the Generalized Hermite Polynomials

We investigate the Fp,2 Dunkl transform of generalized Hermite polynomials (GHPs) and obtain their Fp,2 transform explicitly, reducing to the well-known Fourier transform when p=0. By applying Parseval’s identity, we then introduce a new family of orthogonal functions associated with GHPs. We further establish a differential-difference equation and a mixed-type relation satisfied by this family, providing new structural properties.