A numerical experiment related to Zolotarev polynomials for weighted sup-norm

The behavior of the graph of the function Z _n (t) = ∥Z _n ′(·, t)∥/∥Z _n (·, t)∥ is discussed in the case where the functions Z _n (x, t) are the Zolotarev polynomials and the norm is a weighted sup norm. Based on calculations performed for various weights, it is conjectured that the characteristic jump in Z _n (t) in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the midpoint of the interval.