JIPAM

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. Topsøe. Furthermore, $ (beta_n)$ is completely monotone.;


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