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Re: LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)

• To: mathgroup at smc.vnet.net
• Subject: [mg51448] Re: [mg51413] LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 17 Oct 2004 03:06:42 -0400 (EDT)
• References: <200410160820.EAA23725@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 16 Oct 2004, at 17:20, peteraptaker wrote:

> LegendreP[1,1,mu]
> Out[with m4] = -Sqrt[1 - mu^2]
> Out[with m5] = Sqrt[(-1 - mu)/(-1 + mu)]*(-1 + mu)
>
> While this ( and common sense) show they are equal ..
>
> dum = m4 - m5 // FullSimplify
> PowerExpand[dum]
> Out[]= 0
>

Well, it seems to me that the commonsense thing to do in such 
situations is not to rely too much on common sense and even less on 
PowerExpand. In fact your two expressions are certainly not equal:

a[mu_] := -Sqrt[1 - mu^2];
b[mu_] := Sqrt[(-1 - mu)/(-1 + mu)]*(-1 + mu);

a[2]
(-I)*Sqrt[3]

FullSimplify[b[2]]

I*Sqrt[3]


Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/

• References:
  • LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
    • From: psa@laplacian.co.uk (peteraptaker)