# Why does Mathematica not go to specified order in series?

For some reason Mathematica will not evaluate this asymptotic series to the requested order.

Inputting:

1/x ( x ((1 - x)^2) + E^x);
Series[%, {x, \[Infinity], 0}]


Yields:

$\left( x^2 + \frac{1}{\mathcal{O} \left( \frac{1}{x} \right)} \right) + e^x \left( \frac{1}{x} + \mathcal{O} \left( \frac{1}{x} \right)^2 \right)$

The problem being that in the first term it doesn't give me the $\mathcal{O} (x^1)$ and $\mathcal{O} (x^0)$ that I requested.

Mathematica does not make this error for simpler expressions, but I haven't been able to nail down what exactly about this expression is giving me problems.

A couple things I have tried:

(1) I could simply go to a higher order in x in order to get the 'missing' terms, but this is computationally expensive on more complicated expressions.

(2) If I Expand[%] the expression prior to the series expansion that gives me the correct terms, the only thing is, I would never have guessed that I have to put that in there. Plus I often deal with expressions much more complicated than this and it is hard to visually inspect all the $\mathcal{O}(1/\Lambda)$'s all over the place

Is there a simple reason I should have anticipated this being a problem for Mathematica? And is there a simple command to use that doesn't slow things down? - sometimes using Expand[%] prior to doing a computation can slow down when dealing with large expressions.

• Interesting. Not sure if it's a bug or a feature. I'll take a look. – Daniel Lichtblau Jul 28 '14 at 23:00
• @DanielLichtblau, Any News on this? – user9660 Jun 26 '16 at 8:34
• @Louis I don't understand the question. Have you tried the computation in a recent version of Mathematica? Do you obtain an unexpected result? Generally speaking, if you ask someone to revisit a thread from ~2 years ago, it would be a good idea to state specifically what you have checked, in what version, and what is the (presumably unexpected and/or undesired) status you encounter. – Daniel Lichtblau Jun 27 '16 at 16:49