Theoretical study derives explicit Dunkl transforms for generalized Hermite polynomials, revealing new orthogonal function families and differential-difference relations.
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.
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Çekirdek et al. (2026) studied this question.
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