Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Pedersen, Henrik L."'
Autor:
Alzer, Horst, Pedersen, Henrik L.
We prove that the function $g(x)= 1 / \bigl( 1 - \cos(x) \bigr)$ is completely monotonic on $(0,\pi]$ and absolutely monotonic on $[\pi, 2\pi)$, and we determine the best possible bounds $\lambda_n$ and $\mu_n$ such that the inequalities $$ \lambda_n
Externí odkaz:
http://arxiv.org/abs/2406.08932
Autor:
Askitis, Dimitris, Pedersen, Henrik L.
Monotonicity properties of the ratio $$ \log \frac{f(x+a_1)\cdots f(x+a_n)}{f(x+b_1)\cdots f(x+b_n)}, $$ where $f$ is an entire function are investigated. Earlier results for Euler's gamma function and other entire functions of genus 1 are generalise
Externí odkaz:
http://arxiv.org/abs/2107.00905
Autor:
Berg, Christian, Pedersen, Henrik L.
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
Externí odkaz:
http://arxiv.org/abs/2008.06349
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 completely monotonic. This includes the Laplace transform of functions of the f
Externí odkaz:
http://arxiv.org/abs/1905.04131
It is shown that a function $f$ is a generalized Stieltjes function of order $\lambda>0$ if and only if $x^{1-\lambda}(x^{\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\geq 0$, thereby complementing a result due to Sokal. Furthermore, a
Externí odkaz:
http://arxiv.org/abs/1706.00606
We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/1612.02257
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Autor:
Pedersen, Henrik L.
Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are given on the
Externí odkaz:
http://arxiv.org/abs/1309.2167
Autor:
Berg, Christian, Pedersen, Henrik L.
The function $G(x)=(1-\ln x /\ln(1+x))x\ln x$ has been considered by Alzer, Qi and Guo. We prove that $G'$ is completely monotonic by finding an integral representation of the holomorphic extension of $G$ to the cut plane. A main difficulty is caused
Externí odkaz:
http://arxiv.org/abs/1105.6181
Autor:
Berg, Christian, Pedersen, Henrik L.
We show that F_a(x)=\frac{\ln \Gamma (x+1)}{x\ln(ax)} is a Pick function for a\ge 1 and find its integral representation. We also consider the function f(x)=(\frac{\pi^{x/2}}{\Gamma(1+x/2)})^{1/(x\ln x)} and show that \ln f(x+1) is a Stieltjes functi
Externí odkaz:
http://arxiv.org/abs/0912.2185