Functional inequalities for modified Bessel functions

Abstract In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turan-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma–gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research.

• Publication year

  2010

• Venue

  International Journal of Biological Macromolecules

• Publication date

  2010-09-24

• Fields of study

  Mathematics, Chemistry

• Identifiers
  DOI 10.1016/j.exmath.2011.07.001arXiv 1009.4814
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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  2010influential reference
• On Turán type inequalities for modified Bessel functions

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