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Representation of functions analytic in a closed domain by series of rational functions

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Abstract

A method is given for representing functions analytic in a closed Jordan domain by series of the form\(\sum\nolimits_{n = 1}^\infty {\frac{{A_n }}{{z - \alpha _n }}} \) (where the poles αn lie outside the domain) and a bound is obtained for the coefficients An.

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Literature cited

  1. 1.

    T. A. Leont'eva, “Representation of analytic functions by series of rational functions,” Matem. Zametki,2, No. 4, 347–356 (1967).

  2. 2.

    G. M. Goluzin, Geometrical Theory of Functions of a Complex Variable [in Russian], Moscow (1966).

  3. 3.

    J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Colloq. Publ., Vol. 20, American Math. Soc. (1966).

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Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 191–200, August, 1968.

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Leont'eva, T.A. Representation of functions analytic in a closed domain by series of rational functions. Mathematical Notes of the Academy of Sciences of the USSR 4, 606–611 (1968). https://doi.org/10.1007/BF01094960

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Keywords

  • Rational Function
  • Closed Domain
  • Jordan Domain
  • Close Jordan Domain