On the zeros of certain linear differential polynomials
type: Item
instance of: scholarly article
title: On the zeros of certain linear differential polynomials
zbMATH Open document ID: 0712.30032
DOI: 10.1016/0022-247X(90)90271-G
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Let f be a meromorphic function in the plane and let F be given by \[ F=f^{(k)}+a_{k-1}f^{(k-1)}+...+a_ 0f,\quad k\geq 3. \] The authors prove that there is no function f such that fF has no zeros, where \(a_ 1,...,a_{k-1}\) are constants, and \(a_ 0\) is a polynomial of degree one. In the case where the \(a_ j\) are polynomials they classify all functions f such that ff'F has no zeros. Here f has one of the following forms: \[ f=\exp (\int e^ Q+c),\quad f=c(\int e^ Q-b)^{-n}, \] \[ f(z)=(az+b)^{-n},\quad f(z)=\exp (az+b), \] where a,b,c are constants, Q is a polynomial, and n is a positive integer.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 4171304
author: Shi-An Gao
author: James K. Langley
reviewed by: Günter Frank
MaRDI profile type: Publication
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full work available at URL: 0022-247x(90)90271-g
OpenAlex ID: W2069806453
description: scientific article; zbMATH DE number 4171304