== Clarify role of  == 
 The 's are only given for , but the moments of  are supposed to match all the way up to index .  Am I correct that  is an arbitrary parameter which can be varied to give different 's, and hence different 's and so give tight bounds on all or almost all half-lines?  Initial reading of the theorem, I had the impression that you only get information on the  half-lines that come from the roots of ; but since  is not uniquely determined by  it seems the theorem is more powerful than was immediately apparent.  Perhaps the role of ,etc... could be clarified in the article.  I don't have any book that covers this theorem so I don't feel qualified to edit the article.