Abstract
We prove in this note a generalization of a theorem due to G. Herzog on zero-free universal entire functions. Specifically, it is shown that, if a nonnegative integer q and a nonconstant entire function φ of subexponential type are given, then there is a residual set in the class of entire functions with zero-free derivatives of orders q and q + 1, such that every member of that set is universal with respect to φ (D), where D is the differentiation operator.
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This work is supported in part by DGICYT grant PB93-0926.
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Bernal-González, L. On universal entire functions with zero-free derivatives. Arch. Math. 68, 145–150 (1997). https://doi.org/10.1007/s000130050043
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DOI: https://doi.org/10.1007/s000130050043