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

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This paper presents a short survey of convergence results and properties of the Lebesgue function λ m,n (x) for(0, 1, …, m )Hermite-Fejér interpolation based on the zeros of the n th Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λ m,n = max{λ m,n (x) : −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λ m,n . Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λ m,n (x) if m ≥ 2 is even.