On universal entire functions with zero-free derivatives
type: Item
instance of: scholarly article
title: On universal entire functions with zero-free derivatives
zbMATH Open document ID: 0865.30041
author: L. Bernal-González
published in: Archiv der Mathematik
publication date: 1997-06-12T00:00:00Z
review text: 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 \(\Phi\) of superexponential 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 \(\Phi (D)\), where \(D\) is the differentiation operator.
Mathematics Subject Classification ID: 30D20
Mathematics Subject Classification ID: 47B99
zbMATH DE Number: 950067
zbMATH Keywords: MacLane's theorem
zbMATH Keywords: universal entire functions
zbMATH Keywords: superexponential type
zbMATH Keywords: residual set
zbMATH Keywords: zero-free derivatives
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 950067