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A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions. (English) Zbl 1403.42005

Summary: 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.

MSC:

42A82 Positive definite functions in one variable harmonic analysis
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
26D07 Inequalities involving other types of functions
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References:

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