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Summation of Series

  • Carl M. Bender
  • Steven A. Orszag
Chapter

Abstract

When perturbation methods such as those introduced in Chap. 7 are used to solve a problem, the answer emerges as an infinite series, usually involving powers of the perturbation parameter ε. In practice, only the first few terms of this series can be conveniently calculated because the iteration procedure becomes increasingly cumbersome as the order of perturbation theory increases. If the perturbation series converges rapidly, summing the few calculated terms gives a good approximation to the exact solution. However, it is more common for the series to converge slowly, if it converges at all.

Keywords

Taylor Series Richardson Extrapolation Divergent Series Pade Approximants Stieltjes Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 33.
    Baker, G. A., Essentials of Fade Approximants, Academic Press, Inc., New York, 1975.Google Scholar
  2. 34.
    Hardy, G. H., Divergent Series, Oxford University Press, Oxford, 1956.Google Scholar
  3. 35.
    Knopp, K., Theory and Application of Infinite Series, Hafner Publishing Company, New York, 1947.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Carl M. Bender
    • 1
  • Steven A. Orszag
    • 2
  1. 1.Department of PhysicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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