[Date Index] [Thread Index] [Author Index]
Re: question: How to get Mathematica to show more than one value of a complex valued function?
On 14 Feb 2004, at 03:56, steve_H wrote: > hello; > > this is Mathematica 5.0 > > given a multi-valued complex function, how can I get Mathematica to > show > more than one value? or to show the general formula for all solutions? > > for example, (-i)^i is multivalued. The result returned by > Mathematica is > Exp[Pi/2], which is the first possible value. But there are infinitly > many > others (if my math is correct), such as Exp[-3/2 Pi], Exp[5/2 Pi] > etc... > where the general function value is Exp[Pi/2 +- 2 n Pi] > n=0,1,2,3,.... > > Same as for Log[z] where z is a complex number, which is multi-valued. > > or can I at least tell Mathematica to tell me if the result returned > is the ONLY > one possible, (i.e. the complex function is NOT multi-valued)? becuase > right now it is not clear from the result if result returned is the > only > value or if there are others. > > thanks, > Steve > Mathematica returns in such cases the so called principal value. However, in version 5 you can get multivalued answer by using: Reduce[x^I == -I, x] C $B":(B Integers && x == E^((-I)*(2*I*Pi*C - (I*Pi)/2)) etc Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/