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These can easily be evaluated using the Taylor series discussed in the
last section, expanded around the origin
, and are an alternative
way of seeing that
. In the case of exponential and
trig functions, the expansions converge for all
, not just small ones
(although they of course converge faster for small ones).
Depending on where you start, these can be used to prove the relations
above. They are most useful for getting expansions for small values of
their parameters. For small x (to leading order):
We will use these fairly often in this course, so learn them.
Next: An Important Relation
Up: Complex Numbers and Harmonic
Previous: Trigonometric and Exponential Relations
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Robert G. Brown
2011-04-19