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 > answer'? 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/ >> >> > >
- References:
- LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
- From: psa@laplacian.co.uk (peteraptaker)
- LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)