A Chebyshev polynomial rate-of-convergence theorem for Stieltjes functions
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
-  J. Abramowitz & I. Stegun, Eds., Handbook of Mathematical Functions, Dover, New York, 1965.
-  George A. Baker Jr., Essentials of Padé approximants, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0454459
-  Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Book Co., New York, 1978. International Series in Pure and Applied Mathematics. MR 538168
-  John P. Boyd, The rate of convergence of Chebyshev polynomials for functions which have asymptotic power series about one endpoint, Math. Comp. 37 (1981), no. 155, 189–195. MR 616371, https://doi.org/10.1090/S0025-5718-1981-0616371-3
-  John P. Boyd, The optimization of convergence for Chebyshev polynomial methods in an unbounded domain, J. Comput. Phys. 45 (1982), no. 1, 43–79. MR 650425, https://doi.org/10.1016/0021-9991(82)90102-4
-  H. Cabannes (ed.), Padé approximants method and its applications to mechanics, Springer-Verlag, Berlin-New York, 1976. Lecture Notes in Physics, Vol. 47. MR 0494843
-  David Gottlieb and Steven A. Orszag, Numerical analysis of spectral methods: theory and applications, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1977. CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26. MR 0520152
-  P. Graves-Morris, Ed., Padé Approximants, Institute of Physics, London, 1973.
-  P. R. Graves-Morris (ed.), Padé approximants and their applications, Academic Press, London-New York, 1973. MR 0435681
-  Yudell L. Luke, Chebyshev expansions and rational approximations, J. Comput. Appl. Math. 2 (1976), no. 2, 85–93. MR 0425446, https://doi.org/10.1016/0771-050X(76)90013-9
-  Yudell L. Luke, The special functions and their approximations, Vol. I, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York-London, 1969. MR 0241700
- J. Abramowitz & I. Stegun, Eds., Handbook of Mathematical Functions, Dover, New York, 1965.
- G. Baker, Jr., Essentials for Padé Approximants, Academic Press, New York, 1975. MR 0454459 (56:12710)
- C. Bender & S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978. MR 538168 (80d:00030)
- J. Boyd, "The rate of convergence of Chebyshev polynomials for functions which have asymptotic power series about one endpoint," Math. Comp., v. 37, 1981, pp. 189-195. MR 616371 (82h:41022)
- J. Boyd, "The optimization of convergence for Chebyshev polynomial methods in an unbounded domain," J. Comput. Phys., 1982. (To appear.) MR 650425 (83d:65073)
- H. Cabannes, Ed., Padé Approximants Method and Its Application to Mechanics, Springer-Verlag, Berlin, 1973. MR 0494843 (58:13627)
- D. Gottlieb & S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, Pa., 1977. MR 0520152 (58:24983)
- P. Graves-Morris, Ed., Padé Approximants, Institute of Physics, London, 1973.
- P. Graves-Morris, Ed., Padé Approximants and Their Applications, Academic Press, New York, 1973. MR 0435681 (55:8639)
- Y. L. Luke, "Chebyshev expansions and rational approximations," J. Comput. Appl. Math., v. 2, 1976, pp. 85-95. MR 0425446 (54:13401)
- Y. Luke, The Special Functions and Their Approximations, Vol. I, Academic Press, New York, 1969. MR 0241700 (39:3039)
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