Functional inequalities for modified Bessel functions

Details Functional inequalities for modified Bessel functions Functional inequalities for modified Bessel functions

2010-09-24

arxiv.org/abs/1009.4814v2

Expositiones Mathematicae 29(4) (2011) 399-414

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

10.1016/j.exmath.2011.07.001

In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Tur\'an 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.

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