I haven't tried your example, so I am guessing what you are doing.  BUT...
You could read about how other computer algebra systems deal with this 
problem.
For example Maxima has two methods for multiple-variable series, 
 recursive-by-variable or
total-degree truncation.

I think it is ok to check to see if other people have figured out what to 
do.

RJF

On Monday, June 16, 2014 1:47:07 PM UTC-7, Klaus Santor wrote:
>
> The current method for two variable expansion is to make two one 
> dimensional expansions after removing (via removeO()) the order term for 
> the first expansion. This isn't entirely satisfactory since there is then 
> no proper error term for the two variable expansion. However, the technique 
> does work for getting a series expansion of an explicit function of two 
> variables (without error term). My issue is that it fails completely for an 
> expansion of a general f(x,y). One dimensional expansions work fine for 
> f(x) so that's not the concern. Here is an example that fails:
> f(x,y).series(x,0,3).removeO().series(y,0,3).removeO().
> Is there any way around this failure?
>

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