The third and fourth kinds of Chebyshev polynomials and best uniform approximation. (English) Zbl 1255.41015

Eslahchi, M. R.; Dehghan, Mehdi; Amani, Sanaz

Math. Comput. Modelling 55, No. 5-6, 1746-1762 (2012).

Summary: Using the properties of third and fourth kinds of Chebyshev polynomials, we explicitly determine the best uniform polynomial approximation out of \(P_{n}\) to classes of functions that are obtained from their generating function and their derivatives. Efficiency of these polynomials is demonstrated by some examples.

MSC:

41A50	Best approximation, Chebyshev systems
41A10	Approximation by polynomials
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

best polynomial approximation; alternating set; Chebyshev polynomials; uniform norm

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