A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions
In this paper, we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions of the second kind. As applications, we prove the logarithmically monotonicity for a class of functions involving the modified Bessel functions of second kind and we established new inequalities for this function.
KeywordsBessel functions Positive definite functions Completely monotonic functions Logarithmically completely monotonic functions
Mathematics Subject Classification42A82 33C10 26D07
- 2.Bell, W.W.: Special Functions for Scientists and Engineers, London 1967. Encyclopedia of Mathematics and Its Application, vol. 35. Cambridge Univ. Press, Cambridge (1990)Google Scholar
- 3.Bochner, S.: Integral Transforms and Their Applications, Applied Math. Sciences, vol. 25. Springer, New YorkGoogle Scholar
- 5.Derrien, F.: Strictly positive definite functionsd on the real line, hal-00519325, version 1-20sep (2010)Google Scholar