Orthogonal polynomials-centroid of their zeroes

Let c (n,k) (k=1,...,n) the n zeroes of the monic orthogonal polynomials family P (n) (x). The centroid of these zeroes: controls globally the distribution of the zeroes, and it is relatively easy to obtain information on s (n) , like bounds, inequalities, parameters dependence, ..., from the links between s (n) , the coefficients of the expansion of P (n) (x), and the coefficients beta (n) , gamma (n) in the basic recurrence relation satisfied by P (n) (x). After a review of basic properties of the centroid on polynomials, this work gives some results on the centroid of a large class of orthogonal polynomials.