I was searching for some results for the log-concavity of the modified Bessel function of a second type, but I failed. Has there been any known work on this? I am not even sure if it is the modified Bessel function of a second kind is indeed log-concave or not.



Log-concavity of the modified Bessel function of a second kind
Theorem 2(b) in [1] is equivalent to log-convexity of $K\_\nu$ for every $\nu$. This is said to be "well-known", and three references are given.


[1] Árpád Baricz, Saminathan Ponnusamy, Matti Vuorinen, *Functional inequalities for modified Bessel functions*, [DOI:10.1016/j.exmath.2011.07.001](https://doi.org/10.1016/j.exmath.2011.07.001), [arXiv:1009.4814](https://arxiv.org/abs/1009.4814)


