How to Find Non-Analytic Terms in an Expansion?

[jdstokes]

Suppose I have some expression. The analytic terms in its expansion can always be found from the coefficients of the Taylor expansion. What about the non-analytic terms? Is there some systematic way to obtain them?

 

[lurflurf]

Analytic in what sense? How systematic you can be depends on how general and nonanalystic the terms are. There are Laurent series so mae you can us that. It may help to use a different type of expansion or other method on the other terms.

 

[Ben Niehoff]

There are many cases where a series begins with a logarithm term and then proceeds with the ordinary Taylor series. ln(x) cannot be expanded about x=0, so this is necessary.

This is used to solve differential equations by series substitution. Look up the Frobenius series.