Talk:Chebyshev–Markov–Stieltjes inequalities

$\xi _{i}$ as zeros?

$\xi _{i}$ are the zeros of the polynomials $P_{(}i-1)$?

Clarify role of $c_{2m-1}$

The $c_{i}$'s are only given for $i=1,...2m-2$, but the moments of $\mu$ are supposed to match all the way up to index $i=2m-1$. Am I correct that $c_{2m-1}$ is an arbitrary parameter which can be varied to give different $P_{m}$'s, and hence different $\xi$'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 $m$ half-lines that come from the roots of $P_{m}$; but since $P_{m}$ is not uniquely determined by $c_{1},...c_{2m-2}$ it seems the theorem is more powerful than was immediately apparent. Am I mistaken, or is the statement that $\xi _{1},...\xi _{m}$ are determined by $c_{0},...c_{2m-2}$ false, and that we in fact need $c_{2m-1}$ to determine the $\xi$'s? Perhaps the role of $c_{2m-1}$,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.98.109.176.168 (talk) 05:08, 10 February 2010 (UTC)

I am sorry, I only saw this now. Is the problem fixed in the current version? Sasha (talk) 20:44, 12 December 2011 (UTC)

Polynomial normalization

The article doesn't mention how the orthogonal polynomials are to be normalized - should the polynomials be orthonormal? Please include this information in the article. Obsolesced (talk) 10:05, 2 February 2017 (UTC)