Question: series and csgn

1. The general case (the first output) is fine, but the second output is wrong. Surprisingly, replacing series(ee, ...) with series(sqrt(1/x)*erf(sqrt(x)), ...) does something different:

ee := sqrt(1/x)*erf(sqrt(x));

series(ee, x = 0, 2);
% assuming x < 0;
             -2/sqrt(Pi)+2*x/(3*sqrt(Pi))+O(x^2)

series(ee, x = 0, 2) assuming x < 0; # wrong
              2/sqrt(Pi)-2*x/(3*sqrt(Pi))+O(x^2)

series(sqrt(1/x)*erf(sqrt(x)), x = 0, 2) assuming x < 0;
Error, (in assuming) when calling '`series/signum`'. Received: 'no series at 0'

2. Should Maple be able to handle nested discontinuities? The constant term here is incorrect, so the remainder is not O(z^2).

series(ln(I*ln(-1+z)), z = 0, 2);
         ln(Pi)-(1/2*I)*csgn(ln(-1+z))*(csgn(I*(-1+z))+1)*Pi-I*csgn(I*(-1+z))*z/Pi+O(z^2)

3. This is wrong (it would mean that I^z is unbounded for large positive z):

series(a^z, z = infinity, 2);
                exp((1/2*I)*z*(1-signum(a))*Pi)*abs(a)^z

 

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