Approximation properties of the Vallée-Poussin means of partial sums of a mixed series of Legendre polynomials

DOI10.1134/S0001434608090125zbMath1160.41307MaRDI QIDQ2518062

I. I. Sharapudinov

Publication date: 12 January 2009

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Legendre polynomialJacobi polynomialVallée-Poussin meansHermite interpolation polynomialorder of approximation of a function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Approximation by other special function classes (41A30)

Related Items (14)

Special series in Laguerre polynomials and their approximation properties ⋮ Approximation properties of Fourier series of Sobolev orthogonal polynomials with Jacobi weight and discrete masses ⋮ On representation of a solution to the Cauchy problem by a Fourier series in Sobolev-orthogonal polynomials generated by Laguerre polynomials ⋮ Unnamed Item ⋮ Sobolev-orthogonal systems of functions associated with an orthogonal system ⋮ Approximation properties of the Vallée-Poussin means similar to the partial sums of Fourier series in Laguerre-Sobolev polynomials ⋮ Sobolev orthogonal polynomials associated with Chebyshev polynomials of the first kind and the Cauchy problem for ordinary differential equations ⋮ Sobolev Orthogonal Polynomials Generated by Meixner Polynomials ⋮ Approximation of analytic functions by universal Vallee-Poussin sums on the Chebyshev polynomials ⋮ Sobolev orthogonal polynomials generated by Jacobi and Legendre polynomials, and special series with the sticking property for their partial sums ⋮ The Valleé-Poussin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums ⋮ Sobolev-orthogonal systems of functions and some of their applications ⋮ Approximation Properties of Vallée Poussin Means for Special Series of Ultraspherical Jacobi Polynomials ⋮ Fractal Sobolev systems of functions associated with orthonormal systems of functions

Cites Work

• Unnamed Item
• Approximation of functions of variable smoothness by Fourier-Legendre sums
• Approximation properties of mixed series in terms of Legendre polynomials on the classes $ {W^r}$

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