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

• To: mathgroup at smc.vnet.net
• Subject: [mg51413] LegendreP (Symbolic) is different in Mathematica5 than previous versions (M4, M3 ..)
• From: psa at laplacian.co.uk (peteraptaker)
• Date: Sat, 16 Oct 2004 04:20:54 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```LegendreP gives answers in a different form in Mathematica5 than
Mathematica4 (and, from memory, all previous versions). Simplifying
the new form to the 'nicer' previous one seems 'tough'.

Any ideas, and will this be changed in the latest M5?

[While I have loads of more compex expressions derived from from
LegendreP which are now'a mess' with M5 it seems best to start at the
simplest]

In:=
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

.. I am far from a strategy for useful general simplification.

In:=
{m4,m5}//PowerExpand//FullSimplify//InputForm

Out//InputForm=
{-Sqrt[1 - mu^2], Sqrt[-1 - mu]*Sqrt[-1 + mu]}

```

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