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

• To: mathgroup at smc.vnet.net
• Subject: [mg51478] Re: [mg51413] LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 19 Oct 2004 02:55:53 -0400 (EDT)
• References: <200410160820.EAA23725@smc.vnet.net> <DCE69724-1F76-11D9-9EF0-000A95B4967A@mimuw.edu.pl> <004e01c4b516\$ed91f490\$e06c4ed5@lap5100>
• Sender: owner-wri-mathgroup at wolfram.com

```On 18 Oct 2004, at 22:32, Peter S Aptaker wrote:

> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> Thanks. As with much or most use of LegendreP the argument  mu is real.

Since LegendreP is a polynomial this is not an issue. If two
polynomials are equal for all real values of the argument they have to
be also equal for all complex values.

>  My
> point and concern is in the Subject:
>
> "LegendreP (Symbolic) is different in Mathematica5 than previous
> versions
> (M4, M3 ..)"
>
> Your comment means taht the M5 result is not simply 'a different form'
>  but 'the wrong

It seems so.  Note that if you simply define your own associated
Legendre function using the definition given in Mathematica's help:

P[n_, m_, x_] := (-1)^m*(1 - x^2)^(m/2)*D[LegendreP[n, x], x]

then

P[1, 1, x]

-Sqrt[1 - x^2]

which is the answer v, 4 gives. So it seems that there is a bug in
Mathematca 5, although it seems only to affect the associated Legendre
function and not Legendre polynomial itself.

Andrzej Kozlowski

>
> Peter
>
>
> ----- Original Message ----- From: "Andrzej Kozlowski"
To: mathgroup at smc.vnet.net
> <akoz at mimuw.edu.pl>
> To: "peteraptaker" <psa at laplacian.co.uk>
> Cc: <mathgroup at smc.vnet.net>
> Sent: Saturday, October 16, 2004 2:25 PM
> Subject: [mg51478] Re: [mg51413] LegendreP (Symbolic) is different in
> Mathematica5
> than previous versions (M4, M3 ..)
>
>
>> *This message was transferred with a trial version of CommuniGate(tm)
>> Pro*
>> 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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