>>>>> "gosei" == go furuya writes:
gosei> Hi Raimond
>> I've looked a bit more at this. A simpler example is
>>
>> limit(log(-1-%i*x),x,0,plus);
>>
>> Maxima returns log(-1) = %i*%pi. However, the correct answer is
>> -%i*%pi because we're always in the third quadrant.
gosei> You may confused calculating limit in 2D with 1D.
gosei> In case of uniformization,both %i*%pi and -%i*%pi shoud be correct.
gosei> All that is required is to select domain of uniformization
gosei> ,such that principal value.
What does uniformization mean? And why are they both correct? What
do you mean limit in 2D vs 1D?
Perhaps I'm wrong in assuming log means principal log so the branch
cut is the negative real axis.
Anyway, my reasoning is this:
log(-1-%i*x) = 1/2*log(x^2+1) + %i*arg(-1-%i*x)
As x -> 0 from above, the realpart has limit 0. For the imaginary part
arg(-1-%i*x) is -pi + eps for small x > 0, so the limit is -pi.
Thus the correct answer should be -%i*%pi.
Ray