Series

The typical method of finding a series expansion is to enter the complete expression as in Series[(x+2)Sin[x],{x,0,5}]. or . A seldom documented trick is to get the same series expansions using the cells below.

You can often use Series to find an asymptotic expansion provided one exists

for the function in question. An asymptotic expansion is one where the error

gets smaller as the argument approaches infinity. Series will try to find an

asthmatic expansion if you ask for a series about infinity. The next cell

gives an asthmatic expansion of Erfc[x].

The next cell gives an asthmatic expansion of ArcTan[x].

It turns out you must first use TrigToExp to get an asymptotic expansion of

ArcSinnh[x].

You may need to make a power series in two or three variables and truncate it such that the sum of all exponents in each term is less than or equal to a certain integer. If that is the case download a package I have posted at http://library.wolfram.com/infocenter/MathSource/4950/

Created by Mathematica (May 16, 2004)