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Re: LegendreP of order = -1

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  • Subject: [mg58963] Re: [mg58936] LegendreP of order = -1
  • From: Curtis Osterhoudt <gardyloo at>
  • Date: Mon, 25 Jul 2005 01:12:18 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at


   A contour integration argument shows that, for any integral value of
n (see, e.g., Byron and Fuller's Mathematics of Classical and Quantum
Physics, section 6.9, and recasting into Mathematica's notation),

           LegendreP[ n, 1] = 1;
           LegendreP[ n, -1] = (-1)^n.

Mathematica gets it right.



symbio wrote:

>I'm trying to solve an electrodynamics problem in spherical coordinates and 
>need to use Legendre Polynomials.  Can anyone tell me what is the correct 
>mathematical value for LegendreP[-1,1] supposed to be?  Is it +1 or -1, and 
>more importantly WHY? I have a math book here which says it should be -1, 
>but Mathematica gives +1, so which is correct?
>So the question is: LegendrePolynomial[n = -1, x = 1] = ??? 

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