5 papers
Some two-parameter families of generalized Bernstein functions
Stamatis Koumandos, Henrik L. Pedersen
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 functio…
Special Functions from a Complex Viewpoint
Henrik Laurberg Pedersen
This document contains the lecture notes for a mini-course on special functions from a complex viewpoint given at the OPSFA Summer School OPSFA-S10 2024, in the period July 29th --…
Approximations of generalized Bernstein functions
Stamatis Koumandos, Henrik Laurberg Pedersen
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order…
Higher order Thorin-Bernstein Functions
Henrik Laurberg Pedersen, Stamatis Koumandos
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as…
On the asymptotic behaviour of the quantiles in the gamma distribution
Henrik Laurberg Pedersen
The asymptotic behaviour of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behaviour at infinity are given.