Summation of Series

Carl M. Bender and Steven A. Orszag
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Carl M. Bender: Washington University, Department of Physics
Steven A. Orszag: Yale University, Department of Mathematics

Chapter Chapter Eight in Advanced Mathematical Methods for Scientists and Engineers I, 1999, pp 368-416 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4757-3069-2_8

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