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In this paper, we explore the complex symmetrical characteristics of weightedcomposition operators $W_{u, v}$ and weighted composition-differentiationoperators $W_{u, v, k_1, k_2, \ldots, k_n}$ on the Hardy space$H^2(\mathbb{D}^n)$ over the Polydisk $\mathbb{D}^n$, with respect to thestandard conjugation $\mathcal{J}$. We specify explicit conditions that confirmthe Hermitian characteristics of the operator $W_{u, v, k_1, k_2, \ldots, k_n}$and describe the conditions necessary for it to exhibit normal behavior.Additionally, we identify the kernels of the generalized weightedcomposition-differentiation operators and their corresponding adjointoperators.

Generalized weighted composition operators on Hardy space $H^2(\mathbb{D}^n)$