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MathGroup Archive 2005

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LegendreP error (bug?) in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58892] LegendreP error (bug?) in Mathematica
  • From: "ab at sd.com" <at2 at ads.com>
  • Date: Fri, 22 Jul 2005 01:58:42 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Why does Mathematica give an erroneous answer to LegendreP[-1,1]=1? where it 
shoudl give -1 according to the series expansion below? is this a bug?

In[13]:=
LegendreP[-1, 1]
Out[13]=
1
In[12]:=
p[n_, z_] = (-1)^n*
Sum[((Pochhammer[-n, k]*Pochhammer[n + 1, k])/k!^2)*
((z + 1)/2)^k, {k, 0, n}]
Out[12]=
n z + 1
(-1) Hypergeometric2F1[-n, n + 1, 1, -----]
2
In[16]:=
p[-1, 1]
Out[16]=
-1


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