Christian Berg

Publications (8)1.13 Total impact

• Source

  Available from: ArXiv

  Article: A completely monotonic function used in an inequality of Alzer

  Christian Berg, Henrik L. Pedersen
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  ABSTRACT: 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 by the fact that $G'$ is not a Stieltjes function.
  05/2011;
• Source

  Available from: ArXiv

  Article: A Pick function related to the sequence of volumes of the unit ball in n-space

  Christian Berg, Henrik L. Pedersen
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  ABSTRACT: 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 function and that f(x+1) is completely monotonic on (0,\infty). In particular f(n)=\Omega_n^{1/(n\ln n)},n\ge 2 is a Hausdorff moment sequence. Here \Omega_n is the volume of the unit ball in Euclidean n-space
  12/2009;
• Article: Nevanlinna Matrices of Entire Functions

  Christian Berg, Henrik L. Pedersen
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  ABSTRACT: The notion of a pre-Nevanlinna matrix of entire functions is introduced, and we find necessary and sufficient conditions for an entire function to belong to such a matrix, thereby generalizing previous work of Krein.If one of the functions in a pre-Nevanlinna matrix is a polynomial, then the three others arc also polynomials and their degrees differ by at most two. If the functions in a pre-Nevanlinna matrix are transcendental they have necessarily the same order, type and indicators.
  Mathematische Nachrichten 11/2006; 171(1):29 - 52. · 0.68 Impact Factor
• Source

  Available from: ArXiv

  Article: Convexity of the median in the gamma distribution

  Christian Berg, Henrik L. Pedersen
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  ABSTRACT: We show that the median $m(x)$ in the gamma distribution with parameter $x$ is a strictly convex function on the positive half-line
  10/2006;
• Source

  Available from: ArXiv

  Article: The Chen-Rubin conjecture in a continuous setting

  Henrik L. Pedersen, Christian Berg
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  ABSTRACT: We study the median in the Gamma distribution as a function of the parameter. Using methods from complex analysis we show that the derivative of the median is less than 1 and we thereby solve a conjecture of Chen and Rubin from 1986. We also study the asymptotic behaviour of the median at infinity and at zero.
  12/2004;
• Source

  Available from: kryakin.com

  Article: On the order and type of the entire functions associated with an indeterminate Hamburger moment problem

  Christian Berg, Henrik L. Pedersen
  Arkiv för matematik 02/1994; 32(1):1-11. · 0.45 Impact Factor
• Source

  Available from: psu.edu

  Article: Pick Functions Related to the Gamma Function

  Christian Berg, Henrik L. Pedersen
• Source

  Available from: citeseerx.ist.psu.edu

  Article: A completely monotone function related to the Gamma function

  Christian Berg, Henrik L. Pedersen
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  ABSTRACT: We show that the reciprocal of the functionis a Stieltjes transform. As a corollary we obtain that the derivative of f is completely monotone, in the sense that (−1)n−1f(n)(x)⩾0 for all n⩾1 and all x>0. This answers a question raised by Dimitar Dimitrov at the Fifth International Symposium on Orthogonal Polynomials, Special Functions and Applications held in Patras in September 1999. To prove the result we examine the imaginary part of 1/f in the upper half-plane, in particular close to the negative real axis, where Stirling's formula is not valid.
  Journal of Computational and Applied Mathematics.