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The Quarterly Journal of Mechanics and Applied Mathematics 1974 27(4):423-450; doi:10.1093/qjmam/27.4.423
© 1974 by Oxford University Press
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ANALYSIS AND IMPROVEMENT OF PERTURBATION SERIES

MILTON VAN DYKE

( Stanford University Stanford, California )

A battery of techniques is discussed for exploring the analytic structure of the solution of a physical problem derived as a formal power series, and then extending its range of utility. The nearest singularity is usually revealed by a graphical ratio test due to Domb and Sykes. According as that singularity lies on the positive real axis or elsewhere, various transformations can be applied to accelerate the convergence of the series. These techniques are demonstrated by application to a number of examples, drawn mainly from fluid mechanics.


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