Some two-parameter families of generalized Bernstein functions

2025/07/04 by Koumandos, Stamatis, Pedersen, Henrik L.
#44A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.03551

Abstract

We prove that certain functions involving ratios of Gamma functions and the Psi-function belong to generalized Bernstein classes and new properties of generalized Bernstein functions are given.

Citations

• Higher order Thorin-Bernstein Functions
• Ratios of Entire functions and generalized Stieltjes functions
• Completely monotonic ratios of basic and ordinary gamma functions
• Nielsen's beta function and some infinitely divisible distributions
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function

Related

• Approximations of generalized Bernstein functions
• Higher order Thorin-Bernstein Functions
• On properties of Bernstein functions of several complex variables
• A family of Horn-Bernstein functions
• Some results on Bernstein-Sato polynomials for parametric analytic functions