Consider the Dunkl Laplacian \(\Delta _k\) associated with a root system \(\Phi \) in \(\mathbb {R}^d\) and a nonnegative multiplicity function k on \(\Phi \) . In this work, we introduce a generalized Vekua integral transform \(\mathcal {M}_{\frac{d}{2}+\gamma }\) within the Dunkl setting, where \(2\gamma :=\sum _{\alpha \in \Phi }k(\alpha )\) is the sum of multiplicities. We prove that \(\mathcal {M}_{\frac{d}{2}+\gamma }\) and its inverse establish a one-to-one correspondence between \(\Delta _k\) -harmonic functions and solutions to the \(\Delta _k\) -Helmholtz equation. As an application, we describe \(\Delta _k\) -metaharmonic functions on the unit ball by expressing them in terms of homogeneous \(\Delta _k\) -harmonic polynomials and the normalized Bessel function. Moreover, we obtain analogous results for Dunkl polyharmonic operator.
