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On the numerical analytic continuation of power series

Part of the Lecture Notes in Mathematics book series (LNM,volume 571)

Keywords

  • Power Series
  • Euler Method
  • Geometric Series
  • Summation Method
  • Precision Arithmetic

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References

  1. Henrici, P., An algorithm for analytic continuation, SIAM J. Num. Anal. 3 (1966), 67–78.

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  2. Henrici, P., Applied and computational complex analysis, Vol. I, John Wiley, New York, 1974.

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  3. Klewin, R., Über die Anwendbarkeit von allgemeinen Euler-Verfahren bei der analytischen Fortsetzung, Dissertation, Universität Mannheim, 1974.

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  4. Niethammer, W., Ein numerisches Verfahren zur analytischen Fortsetzung, Num. Math. 21 (1973), 81–92.

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  5. Niethammer, W. and U. Schweitzer, On the numerical analytic continuation of power series with application to the two-body and three-body problems, Comput. Meth. in Appl. Mech. and Eng. 5 (1975), 239–249.

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  6. Powell, R.E. and S.M. Shah, Summability theory and applications, Van Nostrand, London, 1972.

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  7. Schweitzer, U., Über die Anwendung von Summationsmethoden bei der numerischen Lösung des Zwei-und Drei-Körper-Problems, Dissertation, Universität Mannheim, 1974.

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  8. Zeller, K. and W. Beekmann, Theorie der Limitierungsverfahren, Springer, Berlin-Heidelberg-New York, 1970.

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  9. Zelmer, G.K., Summation methods in the two-and three-body problems, Thesis, University of British Columbia, 1967.

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  10. Zelmer, G.K., (E,γ,α,β)-Summability and applications, Arch. Rat. Mech. Anal. 35 (1969), 211–219.

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© 1977 Springer-Verlag Berlin · Heidelberg

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Niethammer, W. (1977). On the numerical analytic continuation of power series. In: Schempp, W., Zeller, K. (eds) Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086572

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  • DOI: https://doi.org/10.1007/BFb0086572

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08069-5

  • Online ISBN: 978-3-540-37496-1

  • eBook Packages: Springer Book Archive