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Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. I. Maehly type approximants. (English) Zbl 1071.41012
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.

MSC:
41A20 Approximation by rational functions
41A21 Padé approximation
41A25 Rate of convergence, degree of approximation
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