Geodesic
Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials
Matematičeskie zametki, Tome 84 (2008) no. 3, pp. 452-471

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We estimate the order of weighted approximations of functions and their derivatives by using the means of mixed series of Legendre polynomials. As the main result, we obtain estimates of the order of approximation of a function and its derivatives by the Vallée-Poussin means and their derivatives.
Keywords: approximation of functions, Vallée-Poussin means
Mots-clés : Legendre polynomial, Fourier–Legendre series, Jacobi polynomial, Hermite interpolation polynomial. 
@article{MZM_2008_84_3_a11,
     author = {I. I. Sharapudinov},
     title = {Approximation {Properties} of the {Vall\'ee-Poussin} {Means} of {Partial} {Sums} of a {Mixed} {Series} of {Legendre} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {452--471},
     publisher = {mathdoc},
     volume = {84},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/}
}
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I. I. Sharapudinov. Approximation Properties of the Vall\'ee-Poussin Means of Partial Sums of a Mixed Series of Legendre Polynomials. Matematičeskie zametki, Tome 84 (2008) no. 3, pp. 452-471. http://geodesic.mathdoc.fr/item/MZM_2008_84_3_a11/