# zbMATH — the first resource for mathematics

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.)
Full Text:
##### References:
 [1] Mason, J.C.; Handscomb, D.C., Chebyshev polynomials, (2003), Chapman & Hall/CRC · Zbl 1015.33001 [2] Rivlin, T.J., An introduction to the approximation of functions, (1981), Dover New York · Zbl 0189.06601 [3] Rivlin, T.J., Polynomials of best uniform approximation to certain rational functions, Numer. math., 4, 345-349, (1962) · Zbl 0112.35304 [4] Ollin, H.Z., Best polynomial approximation to certain rational functions, J. approx. theory, 26, 389-392, (1979) · Zbl 0421.41016 [5] Eslahchi, M.R.; Dehghan, M., The best uniform polynomial approximation to class of the form $$1 /(a^2 \pm x^2)$$, Nonlinear anal. TMA, 71, 740-750, (2009) · Zbl 1171.41310 [6] Dehghan, M.; Eslahchi, M.R., Best uniform polynomial approximation of some rational functions, Comput. math. appl., 59, 382-390, (2010) · Zbl 1189.41004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.