Comment #10 on issue 3135 by [email protected]: Multiple series expansions
http://code.google.com/p/sympy/issues/detail?id=3135

The output will change if we assume that x->oo and y->oo, right?

Yes, in this case.

So when doing series, is it assumed that both are tending to 0?

Yes.

Also can you explain what is wrong with the order term in the given example?

In which one?  #6, #7, #8 - all correct.

If you about #1, then the answer is: O term is not for symbol bookkeeping. The only workaround for now: avoid autoevaluation. For example:
In [3]: Mul(O(x**6), exp(y), evaluate=True)
Out[3]:
 ⎛ 6⎞
O⎝x ⎠

In [4]: Mul(O(x**6), exp(y), evaluate=False)
Out[4]:
 ⎛ 6⎞  y
O⎝x ⎠⋅ℯ




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