Convergence and divergence of higher-order Hermite or Hermite-Fejér interpolation polynomials with exponential-type weights. (English) Zbl 1241.41002
Summary: Let , and let , where and is an even function. Then we can construct the orthonormal polynomials of degree for . In this paper for an even integer we investigate the convergence theorems with respect to the higher-order Hermite and Hermite-Fejér interpolation polynomials and related approximation process based at the zeros of . Moreover, for an odd integer , we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros of .
|41A05||Interpolation (approximations and expansions)|
|42C05||General theory of orthogonal functions and polynomials|