Turán determinants of bessel functions

Árpád Baricz, Tibor K. Pogány

Research output: Contribution to journalReview article

15 Citations (Scopus)

Abstract

In this paper first we survey the Turán type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Turán type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulas for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Turán determinants of Bessel functions of the first kind. At the end of the paper we prove a Turán type inequality for the Bessel functions of the second kind.

Original languageEnglish
Pages (from-to)295-322
Number of pages28
JournalForum Mathematicum
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 1 2014

Keywords

  • Bessel functions of the first kind
  • Bessel functions of the second kind
  • Bounds
  • Entire functions
  • Integral representations
  • Laguerre type inequalities
  • Laguerre-Pólya class
  • Neumann series of Bessel functions of the first kind
  • Recurrence relations
  • Turán and Hankel determinants
  • Turán type inequalities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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