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Bounds for the product of modified Bessel functions

Abstract

In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions of the first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of the first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research.

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Correspondence to Árpád Baricz.

Additional information

The research of Á. Baricz was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. S. Ponnusamy is on leave from IIT Madras. The research of S. Singh was supported by the fellowship of the University Grants Commission, India. The authors are grateful to Prof. Tibor K. Pogány for the fruitful discussions during his visit to Babeş-Bolyai University of Cluj-Napoca, Romania, in September 2015.

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Baricz, Á., Maširević, D.J., Ponnusamy, S. et al. Bounds for the product of modified Bessel functions. Aequat. Math. 90, 859–870 (2016). https://doi.org/10.1007/s00010-016-0414-2

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  • DOI: https://doi.org/10.1007/s00010-016-0414-2

Mathematics Subject Classification

  • 39B62
  • 33C10
  • 42A05
  • 44A20

Keywords

  • Modified Bessel functions
  • Turán type inequalities
  • monotonicity properties
  • bounds