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Re: Associated Legendre Definition

• To: mathgroup at smc.vnet.net
• Subject: [mg25641] Re: Associated Legendre Definition
• From: Hendrik van Hees <h.vanhees at gsi.de>
• Date: Wed, 18 Oct 2000 02:52:18 -0400 (EDT)
• Organization: GSI Darmstadt
• References: <8se9qf$6q3@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Preben Bohn wrote:

> P(n,m,x) = (1-x^2)^(m/2) d^m/dx^m (P(n,x))

It's just the problem that there are many different conventions around.
The associated Legendre Polynoms are defined up to a factor of modulus
1. That's clear if you think about them as eigenfunctions of the Casimir
operator of the rotation group SO(3) in quantum mechanics (orbital
angular momentum squared) and the 3-component of the angular momentum.

Y_l^m(theta,phi)=exp(i m phi) P_l^m(cos(theta))

l=0,1,2,... and for given l: m=-l,-l+1,...,l-1,l



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