Re: Explicit Conjugate: a feature or a bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33922] Re: [mg33882] Explicit Conjugate: a feature or a bug?*From*: Roberto Brambilla <rlbrambilla at cesi.it>*Date*: Tue, 23 Apr 2002 07:13:40 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

At 06.12 21/04/02 -0400, you wrote: >Let's consider, say, Version 4.1 . > >Mathematically, the following is alright. >On the other hand, the answer *explicitly* contains Conjugate. > > Integrate[((1 - z)/(-1 + I*z))^(1/3), {z, 0, 1}] > > (-I)*Conjugate[(-1)^(1/3)] + ((1 + I)^(4/3)*Conjugate[(-1)^(1/3)]* > Hypergeometric2F1[1/3, 1/3, 4/3, 1/2 - I/2])/2^(1/3) > > >But Conjugate[(-1)^(1/3)] looks VERY simply: > > Conjugate[(-1)^(1/3)]// ComplexExpand > > -(-1)^(2/3) > > >Thus, Integrate[((1 - z)/(-1 + I*z))^(1/3), {z, 0, 1}] is just > > -(-1)^(1/6) - ((-1)^(2/3)*(1 + I)^(4/3)* > Hypergeometric2F1[1/3, 1/3, 4/3, 1/2 - I/2])/2^(1/3) > >which, as for me, looks much nicer (but, of cause, has the same value). > >Is it a feature or a problem? > > >Vladimir Bondarenko > > >(* P.S. IMHO, this IS a bug because identifying -(-1)^(2/3) is trivial. *) > > > Hi, Vladimir, try this Integrate[((1-z)/(-1+I*z))^(1/3),{z,0,1}]//FullSimplify I obtain with Mathematica4.1 -(-1)^(1/6)+(1/3)(2+2 I)^(1/3) Beta[(1-I)/2,1/3,2/3] which gives the same numerical value 0.436914 - I*0.575664 and looks very fine. Bye, Rob Roberto Brambilla CESI Via Rubattino 54 20134 Milano tel +39.02.2125.5875 fax +39.02.2125.5492 rlbrambilla at cesi.it