\ellk(X) are the fundamental functions of Lagrange interpolation polynomials, \ellk(Xk) =
for a certain absolute constant c > 0. The proof is not very simple and the best value of c is not determined. It seems a reasonable guess that asymptotically (1) is a minimum if the Xi are the roots of the Chebyshev polynomial Tn(X). But we have not been able to prove this.
Classif.: * 41A05 Interpolation
Keywords: Lebesgue function; integration of interpolation functions; Lagrange interpolation polynomials
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