On some conjectures by Morris et al. about zeros of an entire function
type: Item
instance of: scholarly article
title: On some conjectures by Morris et al. about zeros of an entire function
zbMATH Open document ID: 0918.30015
author: Yunkang Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-01T00:00:00Z
review text: Suppose \(y'(t)=-y(qt)\) where \(q\in(0,1)\) and \(y(0)=1\). The only differentiable solution is \(y(t)=\sum^\infty_{n=0} {(-1)^nq^{n(n-1)/2} \over n!}t^n\). The author shows the following: \(t_{n+1}>q^{-1}t_n\) for all \(n\geq 0\) and \(t_{n+1}\leq q^{-2}t_n+1\) for all \(n\geq m\), where \(m\) is the minimal nonnegative integer that obeys \(t_n\geq q^3/(1-q)\), and \(t_0,t_1,\dots\) are the zeros in monotonic increasing order.
reviewed by: Takahiko Nakazi
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 1216726
MaRDI profile type: Publication
Wikidata QID: Q122979735
full work available at URL: jmaa.1998.6054
OpenAlex ID: W2061134587
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DOI: 10.1006/JMAA.1998.6054
description: scientific article; zbMATH DE number 1216726