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  Volume 2, Issue 2, Article 26
 
A Pick Function Related to an Inequality for the Entropy Function
    Authors: Christian Berg,  
    Keywords: Pick functions, completely monotone sequences  
    Date Received: 06/11/00  
    Date Accepted: 06/03/01  
    Subject Codes:

30E20,44A60

  
    Editors: Frank Hansen,  
 
    Abstract:

The function $ psi(z)=2/(1+z)+1/($Log$ (1-z)/2)$, holomorphic in the cut plane $ Bbb Csetminus[1,infty[$, is shown to be a Pick function. This leads to an integral representation of the coefficients in the power series expansion $ psi(z)=sumlimits_{n=0}^inftybeta_nz^n$, $ vert zvert1$. The representation shows that $ (beta_n)$ decreases to zero as conjectured by F. Tops�e. Furthermore, $ (beta_n)$ is completely monotone.

         
       
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