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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
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