Universal Taylor Series in Several Variables Depending on Parameters

Abstract We establish generic existence of Universal Taylor Series on products $$\varOmega = \prod \varOmega _i$$ Ω = ∏ i planar simply connected domains where the universal approximation holds K compact sets with complements provided $$K \cap \emptyset $$ K ∩ ∅ . These classes are respect to one or several centers expansion and is at level functions all derivatives. Also, can be smooth up boundary, that \overline{\varOmega } ¯ $$\{\infty \} \cup [{\mathbb {C}} {\setminus }_i]$$ { ∞ } ∪ [ C \ ] for i All previous kinds series may depend some parameters; then approximable same parameters, as it shown in present paper.