Here we find the order of convergence of the Hermite and Hermite-Fejer interpolation polynomials constructed on the zeros of (1- x^2)P_n(x) where P_n(x) is the Legendre polynomial of degree n with normalization P_n(1)= 1.
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KARADZHOV, G. E., & ADAD, E. E. E. (1997). LOCALIZATION AND SUMMABILITY OF MULTIPLE HERMITE SERIES. International Journal of Mathematics and Mathematical Sciences, 1997(), 61-74. https://doi.org/10.1155/S0161171297000100