A family of Horn-Bernstein functions

TL;DR

This paper revisits a family of Bernstein functions, identifying those with derivatives that are logarithmically completely monotonic, and introduces a new class called Horn-Bernstein functions inspired by Roger A. Horn's work.

Contribution

It defines and characterizes Horn-Bernstein functions, expanding the class of Bernstein functions with specific monotonicity properties.

Findings

Identification of Bernstein functions with logarithmically completely monotonic derivatives

Introduction of the Horn-Bernstein function class

Connections to Roger A. Horn's results

Abstract

A family of recently investigated Bernstein functions is revisited and those functions for which the derivatives are logarithmically completely monotonic are identified. This leads to the definition of a class of Bernstein functions, which we propose to call Horn-Bernstein functions because of the results of Roger A. Horn.