The Lebesgue function for generalized Hermite-Fejer interpolation on the Chebyshev nodes

This paper presents a short survey of convergence results and properties of the Lebesgue function lambda(m,n)(x) for (0, 1,..., m) Hermite-Fejer inter polation based on the zeros of the nth Chebyshev polynomial of the first ki nd. The limiting behaviour as n --> infinity of the Lebesgue constant Lambd a(m,n) = max{lambda(m,n)(x) : -1 less than or equal to x less than or equal to 1} for even m is then studied, and new results are obtained for the asy mptotic expansion of Lambda(m,n). Finally, graphical evidence is provided o f an interesting and unexpected pattern in the distribution of the local ma ximum values of lambda(m,n)(x) if m greater than or equal to 2 is even.