       Re: LegendreP of order = -1

• To: mathgroup at smc.vnet.net
• Subject: [mg58963] Re: [mg58936] LegendreP of order = -1
• From: Curtis Osterhoudt <gardyloo at mail.wsu.edu>
• Date: Mon, 25 Jul 2005 01:12:18 -0400 (EDT)
• References: <200507240521.BAA14443@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Symbio,

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.

C.O.

symbio wrote:

>Hi,
>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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```

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