Comment #8 on issue 3638 by [email protected]: Automatic series expansion while applying a function?
http://code.google.com/p/sympy/issues/detail?id=3638

But we already do things like that for factorial(factorial(1000000000000000000000000000))!

Good point. We should rethink that one. What's a reasonable cutoff for factorial?

I'm not so sure why. All we need is to know in Mul: we want O(x) terms for first operand.
(1+x**2)**1000 * O(x) -> ((1+x**2)**1000).series(x,0,1) * O(x) -> (1+O(x))*O(x)-> O(x)

Yes, it's just a bug. It isn't implemented as smart as it should be.

This isn't implemented, as I sad (cos(x)+O(x**2) should be evaluated first, before Application's eval()). log(1+O(x**2)) - works fine.

log(1 + O(x**2)).series() doesn't work for me.

https://github.com/sympy/sympy/pull/1798 might be related here.

But let's open a new issue for this, because regardless of automatic evaluation, this should work.

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