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Re: LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51490] Re: [mg51413] LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
*From*: "Peter S Aptaker" <psa at laplacian.co.uk>
*Date*: Tue, 19 Oct 2004 02:56:26 -0400 (EDT)
*References*: <200410160820.EAA23725@smc.vnet.net> <DCE69724-1F76-11D9-9EF0-000A95B4967A@mimuw.edu.pl>
*Sender*: owner-wri-mathgroup at wolfram.com
Thanks. As with much or most use of LegendreP the argument mu is real. My
point and concern is in the Subject:
"LegendreP (Symbolic) is different in Mathematica 5 than previous versions
(M4, M3 ..)"
Your comment means ttht the Mathematica 5 result is not simply 'a different form' but
'the wrong
answer'?
Peter
----- Original Message -----
From: "Andrzej Kozlowski" <akoz at mimuw.edu.pl>
To: mathgroup at smc.vnet.net
Subject: [mg51490] Re: [mg51413] LegendreP (Symbolic) is different in Mathematica5
than previous versions (M4, M3 ..)
> 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/
>
>
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