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