Re: Problem with the Derivative of a Arg-function

*To*: mathgroup at smc.vnet.net*Subject*: [mg48637] Re: Problem with the Derivative of a Arg-function*From*: klishko at mail.ru (Alex Klishko)*Date*: Wed, 9 Jun 2004 04:16:54 -0400 (EDT)*References*: <c9k37o$fbo$1@smc.vnet.net> <c9pfq9$t79$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

ab_def at prontomail.com (Maxim) wrote: > The short answer is that the derivative of Arg is undefined: Arg is > not an analytical function. Just consider what happens when you move > along different directions, for example, from 1 to 1+eps and from 1 to > 1+I*eps, with real eps. Yes, you are right. I think that when Mathematica take numerical derivative, it's ought to show error message in case of complex argument (without using ComplexExpand) . > In[1]:= > ComplexExpand[(Arg[z + h] - Arg[z])/h, z, > TargetFunctions -> Abs] // > Limit[#, h -> 0] & // FullSimplify > > Out[1]= > -Im[z]/Abs[z]^2 It's right for real argument, when Re'=1 or dRe[z]=dz It common case it should be (-Im[z]*Re'[z]+Re[z]*Im'[z])/Abs[z]^2 Best wishes Alex Klishko