Explicit Conjugate: a feature or a bug?
- To: mathgroup at smc.vnet.net
- Subject: [mg33882] Explicit Conjugate: a feature or a bug?
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Sun, 21 Apr 2002 06:12:34 -0400 (EDT)
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
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. *)