ca.analysis and odes - Asymptotics for Christoffel number

What is the order for the following sum $sumlimits_{i=1}^{n} frac{lambda _i}{1-x _ i}$ where $lambda _i$-i-th Christoffel number and $x _i$- i-th zero of n-th Legendre polynomial.

P.S
Christoffel number $lambda_ k =intlimits_ {-1}^{1}(frac{p_ n(x)}{p'_ n(x)(x-x_k)})^2 dx$. The problem came from the following one: we want to find maximum value of $frac{(int g(x)dx)^2}{int (1-x)g^2(x)dx}$ over the set of nonnegative on $[-1,1]$ polynomials of degree $n$(not exact value but the order, after using cradrature formula the problem reduced to this one).