# A possible bug of Mathematica

There seems to be a bug for Mathematica when evaluating series expansion for expressions containing log functions. For example:

tmp1=-(1 - x)^2/(-1 + x^2)^2 - ((1 - x)^2 - ((-1 + x)^2*Log[1 - x])/
2)/(-1 + x^2)^2;


When evaluating

Series[tmp1,{x,1,0}]//Normal


I get 0, which is obviously incorrect. To see this, we only need to evaluate

Series[tmp1//Expand,{x,1,0}]//Normal


Has anyone ever met similar problems?

p.s. The version of Mathematica on my PC is "11.0.1 for Linux x86 (64-bit) (September 21, 2016)".

• I think the first result is correct since you ask Mathematica to perform a series expansion that is exact up to order 0, aren't you? – Henrik Schumacher Jan 23 '18 at 15:36
• @ Henrik Schumacher I don't think so, because the first term in "tmp1" is obviously finite up to order 0 in x. – Wen Chern Jan 23 '18 at 15:38
• I see. But Series[tmp1, {x, 1, 0}] returns SeriesData[x, 1, {}, 0, 0, 1] + Log[1 - x] SeriesData[x, 1, {}, 0, 0, 1] and that tells us that there is a singularity. No matter which constant you add. – Henrik Schumacher Jan 23 '18 at 15:42
• On 11.1 I get 1/8 (-4 + Log[1 - x]) for both cases. – John Doty Jan 23 '18 at 15:49
• @JohnDoty Ditto on V11.2. That makes it look like a bug that has been fixed. – Michael E2 Jan 23 '18 at 15:51