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Story of rational approximation for the class of Stieltjes functions: From Stieltjes to recent optimal estimations of errors

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Abstract

We present the history of inequalities for Padé approximant errors in the Stieltjes case. Inequalities optimal in order are obtained for these approximants by using results of J. Vinuesa and A. P. Magnus.

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Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 941–943, July, 1994.

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Gilewicz, J. Story of rational approximation for the class of Stieltjes functions: From Stieltjes to recent optimal estimations of errors. Ukr Math J 46, 1031–1034 (1994). https://doi.org/10.1007/BF01056680

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Keywords

  • Rational Approximation
  • Optimal Estimation
  • Approximant Error
  • Stieltjes Function