Condition numbers of Hankel matrices for exponential weights

We obtain the rate of growth of the largest eigenvalues and Euclidean condition numbers of the Hankel matrices for a general class of even exponential weights W2=exp(−2Q) on an interval I. As particular examples, we discuss Q(x)=α|x| on I=R, and Q(x)=(d2−x2)−α on I=[−d,d].