Asymptotic Behaviour of the Inflection Points of Bessel Functions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Sue Cheun Roderick WONG
  • T. Lang

Detail(s)

Original languageEnglish
Pages (from-to)509-518
Journal / PublicationProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume431
Issue number1883
Publication statusPublished - 8 Dec 1990
Externally publishedYes

Abstract

Asymptotic expansions are derived for the inflection points j$_{\nu k}^{\prime \prime}$ of the Bessel function J$_{\nu}$(x), as k $\rightarrow \infty $ for fixed $\nu $ and as $\nu \rightarrow \infty $ for fixed k. Also derived is an asymptotic expansion of J$_{\nu}$(j$_{\nu k}^{\prime \prime}$) as $\nu \rightarrow \infty $. Finally, we prove that j$_{\nu \lambda}^{\prime \prime}\geq \nu \surd $2 if $\lambda \geq $ (0.07041)$\nu $ + 0.25 and $\nu \geq $ 7, which implies by a recent result of Lorch & Szego that the sequence {$|$J$_{\nu}$(j$_{\nu k}^{\prime \prime}$)$|$} is decreasing, for k = $\lambda $, $\lambda $+1, $\lambda $+2, $\ldots $