The logarithmic concavity of modified Bessel functions of the first kind and its related functions

This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties. One of our results contradicts the conjecture proposed by Neumann in 2007 which states that modifie...

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Bibliographic Details
Published in:Advances in difference equations 2019-09, Vol.2019 (1), p.1-14, Article 379
Main Authors: Nanthanasub, Thanit, Novaprateep, Boriboon, Wichailukkana, Narongpol
Format: Article
Language:English
Subjects:
Analysis
Bessel functions
Bivariate analysis
Concavity
Convexity
Difference and Functional Equations
Functional Analysis
Hypergeometric Function
Kibble’s bivariate gamma distribution
Mathematics
Mathematics and Statistics
Modified Bessel Function
Ordinary Differential Equations
Partial Differential Equations
Probability distribution functions
Proceedings of the International Conference in Mathematics and Applications
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Summary:This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties. One of our results contradicts the conjecture proposed by Neumann in 2007 which states that modified Bessel function of the first kind I ν is log-concave in ( 0 , ∞ ) given ν > 0 . The log-concavity holds true in some bounded domain. The application of the other results in Kibble’s bivariate gamma distribution is also demonstrated.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2309-8