A Family of Horn-Bernstein Functions

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.

Automated summary

This article revisits a family of recently investigated Bernstein functions and identifies those functions with logarithmically completely monotonic derivatives. As a result, a class of Bernstein functions, named Horn-Bernstein functions after Roger A. Horn's findings, is introduced.