A Chebyshev polynomial rate-of-convergence theorem for Stieltjes functions
John P. Boyd
Math. Comp. 39 (1982), 201-206
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Abstract: The theorem proved here extends the author's previous work on Chebyshev series  by showing that if is a member of the class of so-called "Stieltjes functions" whose asymptotic power series about is such that
then the coefficients of the series of shifted Chebyshev polynomials on , satisfy the inequality There is an intriguing relationship between this theorem and a similar rate-of-convergence theorem for Padé approximants of Stieltjes functions which is discussed below.
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