Cross-product of Bessel functions: Monotonicity patterns and functional inequalities

Árpád Baricz, Saminathan Ponnusamy, Sanjeev Singh

Research output: Contribution to journalArticle

Abstract

In this paper, we study the Dini functions and the cross-product of Bessel functions. Moreover, we are interested on the monotonicity patterns for the cross-product of Bessel and modified Bessel functions. In addition, we deduce Redheffer-type inequalities, and the interlacing property of the zeros of Dini functions and the cross-product of Bessel and modified Bessel functions. Bounds for logarithmic derivatives of these functions are also derived. The key tools in our proofs are some recently developed infinite product representations for Dini functions and cross-product of Bessel functions.

Original languageEnglish
Article number36
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume128
Issue number3
DOIs
Publication statusPublished - Jun 1 2018

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Keywords

  • Bessel functions
  • Functional inequalities
  • Redheffer-type inequalities
  • absolutely monotonic and log-concave functions
  • cross-product of Bessel functions
  • infinite product representation
  • interlacing of zeros of Bessel and related functions

ASJC Scopus subject areas

  • Mathematics(all)

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