# Taylor series expansion of arctan(x) around the point 0

This is actually a technical question about why I'm getting different results when trying to do the same thing using Maxima and WolframAlpha.

When I enter

expand arctan(x)

in WolframAlpha I get

$$x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}+\frac{x^9}{9}+O(x^{10})$$

This is what I enter into maxima to get the 5th degree expansion for example

ff:taylor(arctan(x),x,0,5);

The result is littered with terms containing derivative symbols, unlike the nice-looking polynomial WolframAlpha returns.

My question is how to get Maxima to evaluate the expansion at the point 0 and return the first polynomial?

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Repeated differentiation of $\dfrac{1}{1+x^2}$ and evaluation at $x=0$ won't give a $1$. Try it. The second derivative of $\arctan x$ is $0$ at $0$. The third derivative is $-2$ at $x=0$. –  André Nicolas Feb 27 '12 at 14:20
I don't have maxima, and you haven't shown what its output is. But maybe "arctan" is not known to it... perhaps "atan" or something is. –  GEdgar Feb 27 '12 at 15:11