# taylor(1/x^2,x,2,2) give unexpected results

When I calculated this by hand, the constant term is 1/4 but sage gives 3/4.

Sage: $$\newcommand{\Bold}[1]{\mathbf{#1}}\frac{3}{16} {\left(x - 2\right)}^{2} - \frac{1}{4} x + \frac{3}{4}$$

My calculation:

$$\frac{1}{4} -\frac{1}{4}(x-2)+\frac{3}{16}(x-2)^2$$

I'm learning taylor series and sage at the same time, so its quite possible I'm misusing sage. I checked the same thing on wolframalpha, and it agrees with me.

Any ideas? I running sage Sage Version 6.0,Release Date: 2013-12-17 under Ubuntu 12.10. Thanks.

The answer is the same in both cases. If you add 1/4 with 2/4 from the linear term you get 3/4.

Maybe what @Ariyama wants is for Sage to not "simplify" the linear terms.

Yes, if one asks for the Taylor series centered at 2, one should expect the answer to appear with (x-2)'s , not "simplified" into a series with some terms (or just leading term) centered at 2 and the rest centered at 0.