> I know that lseries() cannot do all expressions as nseries(), but it is mostly a matter of implementing the corner cases in there.

Reiterate.  First, they have a different interface.  I don't think we can somewhat emulate logx option for current lseries.  If we want to user lseries() here - that method should properly support logx parameter.

> Another option is to cache nseries. Then when you call it again with a larger n, you simply reuse the cache and compute a few more terms. Then things should be fast.
How about that?

Do you mean to add cacheit decorators for all _eval_nseries methods?