Mason, J. C.; Crampton, A. Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. I. Maehly type approximants. (English) Zbl 1071.41012 Numer. Algorithms 38, No. 1-3, 3-18 (2005). A Padé-type approximants are focused on this paper. The four Chebyshev polynomial types, \(T_n(x),U_n(x),V_n(x)\) and \(W_n(x)\) of degree \(n\) are defined. A Chebyshev series expansion to a given function \(f(x)\) are formed. Laurent series representations of the Maehly type and Padé-Chebyshev approximants are constructed. Numerical examples are applied on all four Padé-Chebyshev approximants. Reviewer: Michael M. Pahirya (Uzhgorod) Cited in 5 Documents MSC: 41A20 Approximation by rational functions 41A21 Padé approximation 41A25 Rate of convergence, degree of approximation Keywords:Chebyshev series; Laurent series; Laurent-Pade approximants; Chebyshev-Padé approximants; Maehly approximants PDF BibTeX XML Cite \textit{J. C. Mason} and \textit{A. Crampton}, Numer. Algorithms 38, No. 1--3, 3--18 (2005; Zbl 1071.41012) Full Text: DOI References: [1] J.S.R. Chisholm and A.K. Common, Generalisations of Padé approximation for Chebyshev and Fourier series, in: Proc. of Internat. Christoffel Symposium (1979) pp. 212-231. [2] C.W. Clenshaw and K. Lord, Rational approximations from Chebyshev series, in: Studies in Numerical Analysis, ed. B.K.P. Skaife (Academic Press, New York, 1974) pp. 95-113. · Zbl 0308.65010 [3] J.A. Fromme and M.A. Golberg, Convergence and stability of a collocation method for the generalised airfoil equation, Appl. Math. Comput.8 (1981) 281-292. · Zbl 0464.65096 · doi:10.1016/0096-3003(81)90023-0 [4] W.B. Gragg and G.D. Johnson, The Laurent?Padé table, in: Information Processing (North-Holland, Amsterdam, 1974) pp. 632-637. · Zbl 0295.65014 [5] H.J. Maehly, Rational approximation for transcendental functions, in: Proc. of IFIP Conference, Butterworths (1960). · Zbl 0112.35303 [6] J.C. Mason, Some applications and drawbacks of Padé approximants, in: Approximation Theory and Applications, ed. Z. Ziegler (1982). [7] J.C. Mason and A Crampton, Laurent?Padé approximants to four kinds of Chebyshev polynomial expansions. Part II: Clenshaw?Lord type approximants, Numer. Algorithms 38 (2005) 19-29. · Zbl 1071.41013 [8] J.C. Mason and D.C. Handscomb, Chebyshev Polynomials ? Theory and Applications (Chapman and Hall/CRC Press, London, 2003). 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.