Author 
Comment/Response 
Tom

07/21/08 10:50am
I am relatively new to Mathematica and relatively bad at mathematics, so this may be all my fault. Still, I've uncovered some mysterious behavior in Series/SeriesCoefficient that seems like a bug to me. Can anyone comment on the problem? I am using Mathematica for Students 6.0.1.0, MacOS X/Intel.
Here is the suspicious behavior. I am trying to find the coefficient for the secondorder term in a Taylor expansion of a simple function around 0.5:
In[1]:= SeriesCoefficient[q Log[1 + xi/(x + c)], {x, 0.5, 2}]
Out[1]= 0
In fact all terms of order higher than 2 have a zero coefficient according to Mathematica. This would be great for my problem, but I don't think it's true. Here I try to find the second order term's coefficient by hand:
In[2]:= FullSimplify[1/(2!) D[q Log[1 + xi/(x + c)], {x, 2}] /. x > 0.5]
Out[2]= (0.5 q xi (1. + 2. c + xi)) / ((0.5 + c)^2 (0.5 + c + xi)^2)
Note that I've modified the output display here: text mode Mathematica won't display properly with the variablewidth font that this forum uses.
Anyway, if you evaluate this result for, say, c>1, xi>1, and q>1, you get a nonzero value, which seems to contradict the results from SeriesCoefficient. What's going on?
I've attached a notebook that presents the same example shown above.
Thanks,
Tom
Attachment: series.nb, URL: , 
