Monotonicity properties of zeros of generalized Airy functions
type: Item
instance of: scholarly article
title: Monotonicity properties of zeros of generalized Airy functions
zbMATH Open document ID: 0681.33008
DOI: 10.1007/BF00945770
author: A. Laforgia
author: Martin E. Muldoon
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: The generalized Airy function is a solution of the differential equation \[ (1)\quad y''+x^{\alpha}y=0,\quad x\in [0,\infty), \] where \(\alpha\) is a positive number. From the introduction: ``M. S. P. Eastham conjectured that the first positive zero \(a_{\alpha 1}\) of a solution of (1) with \(y(0)=0\), decreases as \(\alpha\) increases. We show here that this decrease (to 1) occurs for all positive zeros of such a solution and indeed for all, except possibly the first of the zeros of any nontrivial solution of (1) even without the condition \(y(0)=0.\)''
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34B30
zbMATH DE Number: 4115009
zbMATH Keywords: monotonicity of zeros
zbMATH Keywords: Airy function
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00945770
OpenAlex ID: W1968786977
description: scientific article; zbMATH DE number 4115009