Abstract
Let {z n } be a sequence of complex numbers. We use a generic approach to show the existence of universal entire functions ϕ having several universal properties, i.e. for any pre-assigned compact set K ⊂ ℂ with connected complement and any pre-assigned function f ∈ C(K), holomorphic in the interior of K, there exist: • a suitable sequence of additive translates, • a suitable sequence of multiplicative translates (if 0 ∉ K) and • a suitable sequence of derivatives of ϕ that all converge to f uniformly on K. By a so-called constructive approach, Luh (W. Luh, Entire functions with various universal properties, Complex Var. Theory Appl. 31 (1996), pp. 87–96) obtained functions of this type. In addition, our functions ϕ join two non-universal properties, namely having zeros at certain prescribed points of prescribed order and solving a certain interpolation problem.
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