5 papers · 1 filter
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…
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…
Nielsen's beta function and some infinitely divisible distributions
Christian Berg, Stamatis Koumandos, Henrik L. Pedersen
We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completel…
On generalized Stieltjes functions
Stamatis Koumandos, Henrik L. Pedersen
It is shown that a function is a generalized Stieltjes function of order if and only if is completely monotonic for all , thereby…
Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
Stamatis Koumandos, Henrik L. Pedersen
We introduce completely monotonic functions of order and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma…