ANZIAM J.
44 (2002), 33-40
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Asymptotology---a cautionary tale
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R. L. Dewar
Department of Theoretical Physics and Plasma Research Laboratory
Research School of Physical Sciences and Engineering
Institute of Advanced Studies
The Australian National University
Canberra, ACT 0200
Australia
robert.dewar@anu.edu.au
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Abstract
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The art of asymptotology is a powerful tool in
applied mathematics and theoretical physics, but
can lead to erroneous conclusions if misapplied.
A seemingly paradoxical case is presented in
which a local analysis of an exactly solvable
problem appears to find solutions to an
eigenvalue problem over a continuous range of the
eigenvalue, whereas the spectrum is known to be
discrete. The resolution of the paradox involves
the Stokes phenomenon. The example illustrates
two of Kruskal's Principles of Asymptotology.
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