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/ > >

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