From: //noreply@axelvogt.de   
      
   On 16.04.2017 23:55, Nasser M. Abbasi wrote:   
   ...   
   > Maple rules on ln() are confusing me   
   ...   
      
   Maple respects branch cuts ( = negative axis as   
   default for log and principal branch as default).   
      
      
   ln(z*w) = ln(z)+ln(w)-2*I*Pi*K(ln(z)+ln(w)),   
   ln(z^2) = 2*ln(z)-2*I*Pi*K(2*ln(z)),   
   ln(z^a) = a*ln(z)-2*I*Pi*K(a*ln(z))   
      
   where K is any of the following   
      
   K1:= unapply(unwindK(z),z);   
       = z -> ceil(1/2*(Im(z)-Pi)/Pi)   
   K2:= z -> 1/2*I*(-z+ln(exp(z)))/Pi;   
   K3:= z -> 1/2*(Im(z)-argument(exp(z)))/Pi;   
      
   References:   
   Aslaksen: Can your computer do complex analysis (2005)   
   Davenport, Corless et al: Reasoning about the Elementary   
      Functions of Complex Analysis (2000), TR-00-18.ps   
   Corless, Davenport: According to Abramowitz and Stegun (2002)   
   Corless, Jeffrey: The unwinding number (1996)   
      
   NB: in the references the sign for 'unwinding number'   
   has been changed at some time to the definition now   
   being used in Maple. So take care for the version.   
      
   'unwindK' is a Maple fct, search for 'Wrightomega'   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)