A Family of Horn-Bernstein Functions

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.

KEYWORDS:

• Laplace transform
• Generalized Stieltjes function
• logarithmically completely monotonic function
• Bernstein function

2020 MATHEMATICS SUBJECT CLASSIFICATION MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 44A10
• Secondary: 26A48

Conflict of Interest

No potential conflict of interest was reported by the author(s).