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Summation of Series

In: Advanced Mathematical Methods for Scientists and Engineers I

Author

Listed:
  • Carl M. Bender

    (Washington University, Department of Physics)

  • Steven A. Orszag

    (Yale University, Department of Mathematics)

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.

Suggested Citation

  • Carl M. Bender & Steven A. Orszag, 1999. "Summation of Series," Springer Books, in: Advanced Mathematical Methods for Scientists and Engineers I, chapter 0, pages 368-416, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-3069-2_8
    DOI: 10.1007/978-1-4757-3069-2_8
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