Functional inequalities for modified Bessel functions
Copyright policy )Functional inequalities for modified Bessel functions
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��n 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.
14 pages
- TURUN YLIOPISTO Finland
- University of Turku Finland
- University of Turku Finland
- Department of Mathematics
- TURUN YLIOPISTO Finland
Mathematics(all), convexity, gamma-gamma distribution, ta111, Functional inequalities, Modified Bessel functions, Geometrical convexity, geometrical convexity, 39B62, 33C10, 62H10, Mathematics - Classical Analysis and ODEs, Gamma–gamma distribution, modified Bessel functions, Log-convexity, log-convexity, Classical Analysis and ODEs (math.CA), FOS: Mathematics, functional inequalities, Functional inequalities, including subadditivity, convexity, etc., Turán-type inequality, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Convexity with respect to Hölder means
Mathematics(all), convexity, gamma-gamma distribution, ta111, Functional inequalities, Modified Bessel functions, Geometrical convexity, geometrical convexity, 39B62, 33C10, 62H10, Mathematics - Classical Analysis and ODEs, Gamma–gamma distribution, modified Bessel functions, Log-convexity, log-convexity, Classical Analysis and ODEs (math.CA), FOS: Mathematics, functional inequalities, Functional inequalities, including subadditivity, convexity, etc., Turán-type inequality, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Convexity with respect to Hölder means
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