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AsymptoticSeries

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Description

Summary

A power series in w around w -> 0+, truncated at a known exponent, whose
coefficients are arbitrary expressions not containing w.

Remarks

This is what Gruntz's algorithm expands in, and it is not a Taylor series: the
exponents may be negative and fractional, and the coefficients are symbolic rather
than numeric. What is wanted from it in the end is only the leading term, but the
leading terms of a sum can cancel -- which is the whole point of the algorithm, since
e^(x + e^-x) - e^x cancels to every order when its two parts are expanded separately
-- so the series has to be carried far enough to see past the cancellation, and how
far that is is not known in advance. The caller raises the order until a leading term
survives.
 The value of log(w) is supplied from outside rather than left as a logarithm of
a symbol. Gruntz chooses w as an exponential, so its logarithm is an ordinary
expression in x, and expanding a logarithm needs it: without it the constant term of
log(c * w^e) cannot be told from zero.

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