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Up: The balancing transformation.
Previous: Analyzing
after balancing.
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There is still the question of the amplitude of
. With the
values of a, b, c and d from equation (11) inserted into equation
(7),

Since
lies between
and
, it follows that

Integrating this inequality shows that
behaves like
for some constant K; that is, the amplitude of
decreases to 0 slowly, like
, as
.
Combining our results for
and
we can now say with
certainty that the solutions of Airy's equation behave
like

as
.

Contents
Next: What Happens for
Up: The balancing transformation.
Previous: Analyzing
after balancing.