A function Class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions

TL;DR

This paper explores conditions under which functions related to Bessel functions, especially modified Bessel functions, are positive definite or strictly positive definite, highlighting their properties and relationships with logarithmically completely monotonic functions.

Contribution

It introduces new conditions for positive definiteness of functions related to Bessel functions, expanding understanding of their properties and applications.

Findings

Identifies conditions for positive definiteness of Bessel-related functions

Establishes relationships between logarithmically completely monotonic and positive definite functions

Provides properties and characterizations of modified Bessel functions

Abstract

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.