Entire functions that share a polynomial with one of their derivatives
type: Item
instance of: scholarly article
title: Entire functions that share a polynomial with one of their derivatives
zbMATH Open document ID: 1067.30067
published in: Kodai Mathematical Journal
publication date: 2005-03-30T00:00:00Z
review text: After the work of \textit{L. A. Rubel and C. C. Yang}, [``Value shared by an entire function and its derivative'', Conference of Complex Analysis, University of Kentucky (1976); Lecture Notes in Math., 599, 101--103 (1977; Zbl 0362.30026)] the research on the problem of investigating the relation between an entire function and its derivative became popular. The present paper is also an addition in this direction. In the paper the following result is proved : Let \(f\) be a nonconstant entire function of finite order, \(Q\) be a polynomial with degree \(\geq 1\) and \(k\) be a positive integer. If \(f - Q\) and \(f^{(k)} - Q\) share \(0\) CM then \(f^{(k)} - Q \equiv c( f - Q )\), where \(c\) is a nonzero constant.
reviewed by: Indrajit Lahiri
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 2149311
zbMATH Keywords: meromorphic function
zbMATH Keywords: entire function
zbMATH Keywords: shared value
author: Jianping Wang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1093351321
OpenAlex ID: W1966957731
DOI: 10.2996/KMJ/1093351321
description: scientific article; zbMATH DE number 2149311