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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Truncation errors in Padé approximations to certain functions: An alternative approach


Author: David Elliott
Journal: Math. Comp. 21 (1967), 398-406
MSC: Primary 41.17; Secondary 33.00
MathSciNet review: 0227668
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  • [1] E. W. Cheney and T. H. Southard, A survey of methods for rational approximation, with particular reference to a new method based on a forumla of Darboux, SIAM Rev. 5 (1963), 219–231. MR 0158531 (28 #1754)
  • [2] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, Inc., New York, N. Y., 1948. MR 0025596 (10,32d)
  • [3] Yudell L. Luke, The Padé table and the 𝜏-method, J. Math. and Phys. 37 (1958), 110–127. MR 0099114 (20 #5558)
  • [4] E. Laguerre, ``Sur le réduction en fractions continues, etc.'', J. Math., 4, v. 1, 1885, pp. 135-165.
  • [5] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469 (97k:01072)
  • [6] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953. MR 15, 419.
  • [7] L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, New York, 1960. MR 0107026 (21 #5753)
  • [8] Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR 0106295 (21 #5029)
  • [9] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642 (29 #4914)
  • [10] D. Elliott & B. Robinson, Uniform Asymptotic Estimates of the Classical Orthogonal Polynomials and some Associated Functions, Math. Dept. Tech. Rep. No. 11, University of Tasmania, 1966.
  • [11] F. W. J. Olver, The asymptotic solution of linear differential equations of the second order for large values of a parameter, Philos. Trans. Roy. Soc. London. Ser. A. 247 (1954), 307–327. MR 0067249 (16,695c)
  • [12] N. G. de Bruijn, Asymptotic methods in analysis, Bibliotheca Mathematica. Vol. 4, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1958. MR 0099564 (20 #6003)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1967-0227668-6
PII: S 0025-5718(1967)0227668-6
Article copyright: © Copyright 1967 American Mathematical Society